Answer: True or False? In Exercises 710, determine whether the statement is true

Problem 4E When you use the Fundamental Counting Principle, what are you counting?

Problem 5E Describe the law of large numbers in your own words. Give an example.

Problem 1E What is the difference between an outcome and an event?

Problem 3E Explain why the statement is incorrect: The probability of rain tomorrow is 150%.

In Exercises 80–85, use the following information. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read “2 to 3”) or \(\frac{2}{3}\). The odds of winning an event A are p : q. Show that the probability of event A is given by \(P(A)=\frac{p}{p+q}\) ________________ Equation Transcription: Text Transcription: frac{2}{3} P(A)=frac{p}{p+q}

Determine which of the numbers could not represent the probability of an event. Explain your reasoning. (a) 33.3% (b) -1.5 (c) 0.0002 (d) 0 (e) \(\frac{320}{1058}\) (f) \(\frac{64}{25}\) ________________ Equation Transcription: Text Transcription: frac{320}{1058} frac{64}{25}

Problem 6E List the three formulas that can be used to describe complementary events.

Problem 7E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. You toss a coin and roll a die. The event “tossing tails and rolling a 1 or a 3”

Problem 11E Matching Probabilities In Exercise, match the event with its probability. (a) 0.95 (b) 0.05 (c) 0.25 (d) 0 You toss a coin and randomly select a number from 0 to 9. What is the probability of tossing tails and selecting a 3?

In Exercises 7–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement. A probability of \(\frac{1}{10}\) indicates an unusual event. ________________ Equation Transcription: Text Transcription: frac{1}{10}

Problem 10E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. When an event is almost certain to happen, its complement will be an unusual event.

Problem 8E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth toss is greater than 0.5.

Problem 12E Matching Probabilities In Exercise, match the event with its probability. (a) 0.95 (b) 0.05 (c) 0.25 (d) 0 A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 153?

Problem 14E Matching Probabilities In Exercise, match the event with its probability. (a) 0.95 (b) 0.05 (c) 0.25 (d) 0 Five of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective?

Problem 13E Matching Probabilities In Exercise, match the event with its probability. (a) 0.95 (b) 0.05 (c) 0.25 (d) 0 A game show contestant must randomly select a door. One door doubles her money while the other three doors leave her with no winnings. What is the probability she selects the door that doubles her money?

Problem 15E Identifying a Sample Space In Exercise, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate. Guessing the initial of a student’s middle name

Problem 16E Identifying a Sample Space In Exercise, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate. Guessing a student’s letter grade (A, B, C, D, F) in a class

Problem 17E Identifying a Sample Space In Exercise, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate. Drawing one card from a standard deck of cards

Problem 18E Identifying a Sample Space In Exercise, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate. Tossing three coins

Problem 20E Identifying a Sample Space In Exercise, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate. Rolling a pair of six-sided dice

Problem 19E Identifying a Sample Space In Exercise, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate. Determining a person’s blood type (A, B, AB, O) and Rh-factor (positive, negative)

Problem 21E Identifying Simple Events In Exercise, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning. A computer is used to randomly select a number from 1 to 2000. Event A is selecting the number 253.

Problem 22E Identifying Simple Events In Exercise, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning. A computer is used to randomly select a number from 1 to 4000. Event B is selecting a number less than 500.

Problem 23E Identifying Simple Events In Exercise, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning. You randomly select one card from a standard deck of 52 playing cards. Event A is selecting an ace.

Problem 24E Identifying Simple Events In Exercise, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning. You randomly select one card from a standard deck of 52 playing cards. Event B is selecting the ten of diamonds.

Problem 25E Identifying Simple Events In Exercise, use the Fundamental Counting Principle. Menu A restaurant offers a $12 dinner special that has 5 choices for an appetizer, 10 choices for an entrée, and 4 choices for a dessert. How many different meals are available when you select an appetizer, an entrée, and a dessert?

Problem 26E Identifying Simple Events In Exercise, use the Fundamental Counting Principle. Laptop A laptop has 3 choices for a processor, 3 choices for a graphics card, 4 choices for memory, 6 choices for a hard drive, and 2 choices for a battery. How many ways can you customize the laptop?

Problem 27E Identifying Simple Events In Exercise, use the Fundamental Counting Principle. Realty A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of four digits. The first digit cannot be zero and the last digit must be even. How many different codes are available?

Problem 28E Identifying Simple Events In Exercise, use the Fundamental Counting Principle. True or False Quiz Assuming that no questions are left unanswered, in how many ways can a six-question true or false quiz be answered?

Problem 29E Identifying Simple Events In Exercise, a probability experiment consists of rolling a 12-sided die. Find the probability of the event. Event A: rolling a 2

Problem 30E Identifying Simple Events In Exercise, a probability experiment consists of rolling a 12-sided die. Find the probability of the event. Event B: rolling a 10

Problem 31E Identifying Simple Events In Exercise, a probability experiment consists of rolling a 12-sided die. Find the probability of the event. Event C: rolling a number greater than 4

Problem 32E Identifying Simple Events In Exercise, a probability experiment consists of rolling a 12-sided die. Find the probability of the event. Event D: rolling a number less than 8

Problem 33E Identifying Simple Events In Exercise, a probability experiment consists of rolling a 12-sided die. Find the probability of the event. Event E: rolling a number divisible by 3

Problem 34E Identifying Simple Events In Exercise, a probability experiment consists of rolling a 12-sided die. Find the probability of the event. Event F: rolling a number divisible by 5

Problem 35E Finding Empirical Probabilities A company is conducting a survey to determine how prepared people are for a long-term power outage, natural disaster, or terrorist attack. The frequency distribution at the left shows the results. In Exercise, use the frequency distribution. (Adapted from Harris Interactive) What is the probability that the next person surveyed is very prepared? Response Number of times, f Very prepared 259 Somewhat prepared 952 Not too prepared 552 Not at all prepared 337 Not sure 63

Problem 36E Finding Empirical Probabilities A company is conducting a survey to determine how prepared people are for a long-term power outage, natural disaster, or terrorist attack. The frequency distribution at the left shows the results. In Exercise, use the frequency distribution. (Adapted from Harris Interactive) What is the probability that the next person surveyed is not too prepared? Response Number of times, f Very prepared 259 Somewhat prepared 952 Not too prepared 552 Not at all prepared 337 Not sure 63

Problem 37E Using a Frequency Distribution to Find Probabilities In Exercise, use the frequency distribution at the left, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the age range. (Source: U.S. Census Bureau) 18 to 20 years old Ages of voters Frequency, f(in millions) 18 to 20 4.2 21 to 24 7.9 25 to 34 20.5 35 to 44 22.9 45 to 64 53.5 65 and over 28.3

Problem 39E Using a Frequency Distribution to Find Probabilities In Exercise, use the frequency distribution at the left, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the age range. (Source: U.S. Census Bureau) 21 to 24 years old Ages of voters Frequency, f(in millions) 18 to 20 4.2 21 to 24 7.9 25 to 34 20.5 35 to 44 22.9 45 to 64 53.5 65 and over 28.3

Problem 40E Using a Frequency Distribution to Find Probabilities In Exercise, use the frequency distribution at the left, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the age range. (Source: U.S. Census Bureau) 45 to 64 years old Ages of voters Frequency, f(in millions) 18 to 20 4.2 21 to 24 7.9 25 to 34 20.5 35 to 44 22.9 45 to 64 53.5 65 and over 28.3

Problem 38E Using a Frequency Distribution to Find ProbabilitiesIn Exercise, use the frequency distribution at the left, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the age range. (Source: U.S. Census Bureau) 35 to 44 years old Ages of voters Frequency, f(in millions) 18 to 20 4.2 21 to 24 7.9 25 to 34 20.5 35 to 44 22.9 45 to 64 53.5 65 and over 28.3

Problem 41E Classifying Types of Probability In Exercise, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. According to company records, the probability that a washing machine will need repairs during a six-year period is 0.10.

Problem 42E Classifying Types of Probability In Exercise, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. The probability of choosing 6 numbers from 1 to 40 that match the 6 numbers drawn by a state lottery is 1>3,838,380 ? 0.00000026.

Problem 43E Classifying Types of Probability In Exercise, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. An analyst feels that a certain stock’s probability of decreasing in price over the next week is 0.75.

Problem 44E Classifying Types of Probability In Exercise, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. According to a survey, the probability that a voting-age citizen chosen at random is in favor of a skateboarding ban is about 0.63.

Problem 45E Classifying Types of Probability In Exercise, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. The probability that a randomly selected number from 1 to 100 is divisible by 6 is 0.16.

Problem 47E Finding the Probability of the Complement of an Event The age distribution of the residents of San Ysidro, New Mexico, is shown at the left. In Exercise, find the probability of the event.(Source: U.S. Census Bureau) Event A: randomly choosing a resident who is not 15 to 29 years old Ages Frequency, f 0 –14 38 15 –29 20 30 – 44 31 45 –59 53 60 –74 36 75 and over 15

Problem 48E Finding the Probability of the Complement of an Event The age distribution of the residents of San Ysidro, New Mexico, is shown at the left. In Exercise, find the probability of the event.(Source: U.S. Census Bureau) Event B: randomly choosing a resident who is not 45 to 59 years old Ages Frequency, f 0 –14 38 15 –29 20 30 – 44 31 45 –59 53 60 –74 36 75 and over 15

In Exercises 51–54, a probability experiment consists of rolling a six-sided die and spinning the spinner shown at the left. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the event. Then tell whether the event can be considered unusual. Event A: rolling a 5 and the spinner landing on blue

Problem 50E Finding the Probability of the Complement of an Event The age distribution of the residents of San Ysidro, New Mexico, is shown at the left. In Exercise, find the probability of the event.(Source: U.S. Census Bureau) Event D: randomly choosing a resident who is not 75 years old or older Ages Frequency, f 0 –14 38 15 –29 20 30 – 44 31 45 –59 53 60 –74 36 75 and over 15

In Exercises 51–54, a probability experiment consists of rolling a six-sided die and spinning the spinner shown at the left. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the event. Then tell whether the event can be considered unusual. Event B: rolling an odd number and the spinner landing on green

Problem 46E Classifying Types of Probability In Exercise, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. You think that a football team’s probability of winning its next game is about 0.80.

In Exercises 51–54, a probability experiment consists of rolling a six-sided die and spinning the spinner shown at the left. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the event. Then tell whether the event can be considered unusual. Event C: rolling a number less than 6 and the spinner landing on yellow

In Exercises 51–54, a probability experiment consists of rolling a six-sided die and spinning the spinner shown at the left. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the event. Then tell whether the event can be considered unusual. Event D: not rolling a number less than 6 and the spinner landing on yellow

Problem 55E Security System The access code for a garage door consists of three digits. Each digit can be any number from 0 through 9, and each digit can be repeated. (a) Find the number of possible access codes. ________________ (b) What is the probability of randomly selecting the correct access code on the first try? ________________ (c) What is the probability of not selecting the correct access code on the first try?

Problem 56E Security System An access code consists of a letter followed by four digits. Any letter can be used, the first digit cannot be 0, and the last digit must be even. (a) Find the number of possible access codes. ________________ (b) What is the probability of randomly selecting the correct access code on the first try? ________________ (c) What is the probability of not selecting the correct access code on the first try?

You are planning a three-day trip to Seattle, Washington, in October. In Exercises 57–60, use the tree diagram shown at the left. List the outcome(s) of the event “It rains all three days.”

You are planning a three-day trip to Seattle, Washington, in October. In Exercises 57–60, use the tree diagram shown at the left. List the outcome(s) of the event “It rains on exactly one day.”

Problem 49E Finding the Probability of the Complement of an Event The age distribution of the residents of San Ysidro, New Mexico, is shown at the left. In Exercise, find the probability of the event.(Source: U.S. Census Bureau) Event C: randomly choosing a resident who is not 14 years old or younger Ages Frequency, f 0 –14 38 15 –29 20 30 – 44 31 45 –59 53 60 –74 36 75 and over 15 Step-by-step solution Step 1 of 1 The age distribution of the residents of San Ysidro,

You are planning a three-day trip to Seattle, Washington, in October. In Exercises 57–60, use the tree diagram shown at the left. List the outcome(s) of the event “It rains on at least one day.”

You are planning a three-day trip to Seattle, Washington, in October. In Exercises 57–60, use the tree diagram shown at the left. List the sample space.

In Exercises 61 and 62, use the diagram. What is the probability that a registered voter in Virginia chosen at random voted in the 2012 general election? (Source: Commonwealth of Virginia State Board of Elections)

In Exercises 61 and 62, use the diagram. What is the probability that a voter chosen at random did not vote for a Republican representative in the 2010 election? (Source: Federal Election Commission)

In Exercises 63–66, use the bar graph at the left, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random is a doctorate.

In Exercises 63–66, use the bar graph at the left, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random is a master’s degree.

In Exercises 63–66, use the bar graph at the left, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random is an associate’s degree.

Problem 67E Unusual Events Can any of the events in Exercises be considered unusual? Explain. Using a Frequency Distribution to Find Probabilities In Exercise, use the frequency distribution at the left, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the age range. (Source: U.S. Census Bureau) 18 to 20 years old Ages of voters Frequency, f(in millions) 18 to 20 4.2 21 to 24 7.9 25 to 34 20.5 35 to 44 22.9 45 to 64 53.5 65 and over 28.3 Using a Frequency Distribution to Find Probabilities In Exercise, use the frequency distribution at the left, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the age range. (Source: U.S. Census Bureau) 35 to 44 years old Ages of voters Frequency, f(in millions) 18 to 20 4.2 21 to 24 7.9 25 to 34 20.5 35 to 44 22.9 45 to 64 53.5 65 and over 28.3 Using a Frequency Distribution to Find Probabilities In Exercise, use the frequency distribution at the left, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the age range. (Source: U.S. Census Bureau) 21 to 24 years old Ages of voters Frequency, f(in millions) 18 to 20 4.2 21 to 24 7.9 25 to 34 20.5 35 to 44 22.9 45 to 64 53.5 65 and over 28.3 Using a Frequency Distribution to Find Probabilities In Exercise, use the frequency distribution at the left, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the age range. (Source: U.S. Census Bureau) 45 to 64 years old Ages of voters Frequency, f(in millions) 18 to 20 4.2 21 to 24 7.9 25 to 34 20.5 35 to 44 22.9 45 to 64 53.5 65 and over 28.3

In Exercises 63–66, use the bar graph at the left, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random is a high school diploma.

Can any of the events in Exercises 63–66 be considered unusual? Explain.

A Punnett square is a diagram that shows all possible gene combinations in a cross of parents whose genes are known. When two pink snapdragon flowers (RW) are crossed, there are four equally likely possible outcomes for the genetic makeup of the offspring: red (RR), pink (RW), pink (WR), and white (WW), as shown in the Punnett square at the left. When two pink snapdragons are crossed, what is the probability that the offspring will be (a) pink, (b) red, and (c) white?

There are six basic types of coloring in registered collies: sable (SSmm), tricolor (ssmm), trifactored sable (Ssmm), blue merle (ssMm), sable merle (SSMm), and trifactored sable merle (SsMm). The Punnett square below shows the possible coloring of the offspring of a trifactored sable merle collie and a trifactored sable collie. What is the probability that the offspring will have the same coloring as one of its parents?

In Exercises 71–74, use the pie chart at the left, which shows the number of workers (in thousands) by industry for the United States. (Source: United States Department of Labor) Find the probability that a worker chosen at random was employed in the services industry.

In Exercises 71–74, use the pie chart at the left, which shows the number of workers (in thousands) by industry for the United States. (Source: United States Department of Labor) Find the probability that a worker chosen at random was employed in the manufacturing industry.

In Exercises 71–74, use the pie chart at the left, which shows the number of workers (in thousands) by industry for the United States. (Source: United States Department of Labor) Find the probability that a worker chosen at random was not employed in the services industry.

In Exercises 71–74, use the pie chart at the left, which shows the number of workers (in thousands) by industry for the United States. (Source: United States Department of Labor) Find the probability that a worker chosen at random was not employed in the agriculture, forestry, fishing, and hunting industry.

A stem-and-leaf plot for the numbers of touchdowns scored by all 120 NCAA Division I Football Bowl Subdivision teams is shown. Find the probability that a team chosen at random scored (a) at least 51 touchdowns, (b) between 20 and 30 touchdowns, inclusive, and (c) more than 72 touchdowns. Are any of these events unusual? Explain. (Source: National Collegiate Athletic Association)

An individual stock is selected at random from the portfolio represented by the box-and-whisker plot shown. Find the probability that the stock price is (a) less than $21, (b) between $21 and $50, and (c) $30 or more.

Problem 77E Writing In Exercise, write a statement that represents the complement of the probability. The probability of randomly choosing a tea drinker who has a college degree (Assume that you are choosing from the population of all tea drinkers.)

Problem 78E Writing In Exercise, write a statement that represents the complement of the probability. The probability of randomly choosing a smoker whose mother also smoked (Assume that you are choosing from the population of all smokers.)

Problem 79EC Rolling a Pair of Dice You roll a pair of six-sided dice and record the sum. (a) List all of the possible sums and determine the probability of rolling each sum. ________________ (b) Use technology to simulate rolling a pair of dice and record the sum 100 times. Make a tally of the 100 sums and use these results to list the probability of rolling each sum. ________________ (c) Compare the probabilities in part (a) with the probabilities in part (b). Explain any similarities or differences.

In Exercises 80–85, use the following information. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read “2 to 3”) or \(\frac{2}{3}\). A beverage company puts game pieces under the caps of its drinks and claims that one in six game pieces wins a prize. The official rules of the contest state that the odds of winning a prize are 1 : 6. Is the claim “one in six game pieces wins a prize” correct? Explain your reasoning. ________________ Equation Transcription: Text Transcription: frac{2}{3}

In Exercises 80–85, use the following information. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read “2 to 3”) or \(\frac{2}{3}\). The probability of winning an instant prize game is \(\frac{1}{10}\). The odds of winning a different instant prize game are 1 : 10. You want the best chance of winning. Which game should you play? Explain your reasoning. ________________ Equation Transcription: Text Transcription: frac{2}{3} frac{1}{10}

In Exercises 80–85, use the following information. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read “2 to 3”) or \(\frac{2}{3}\). The odds of an event occurring are 4 : 5. Find (a) the probability that the event will occur and (b) the probability that the event will not occur. ________________ Equation Transcription: Text Transcription: frac{2}{3}

In Exercises 80–85, use the following information. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read “2 to 3”) or \(\frac{2}{3}\). A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is a spade. ________________ Equation Transcription: Text Transcription: frac{2}{3}

In Exercises 80–85, use the following information. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read “2 to 3”) or \(\frac{2}{3}\). A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is not a spade. ________________ Equation Transcription: Text Transcription: frac{2}{3}

What is the difference between an outcome and an event?

Determine which of the numbers could not represent the probability of an event. Explain your reasoning. (a) 33.3% (b) -1.5 (c) 0.0002 (d) 0 (e) 320 1058 (f) 64 25

Explain why the statement is incorrect: The probability of rain tomorrow is 150%.

When you use the Fundamental Counting Principle, what are you counting?

Describe the law of large numbers in your own words. Give an example.

List the three formulas that can be used to describe complementary events.

True or False? In Exercises 710, determine whether the statement is true or false. If it is false, rewrite it as a true statement.. You toss a coin and roll a die. The event tossing tails and rolling a 1 or a 3 is a simple event

True or False? In Exercises 710, determine whether the statement is true or false. If it is false, rewrite it as a true statement.You toss a fair coin nine times and it lands tails up each time. The probability it will land heads up on the tenth toss is greater than 0.5.

True or False? In Exercises 710, determine whether the statement is true or false. If it is false, rewrite it as a true statement.A probability of 1 10 indicates an unusual event.

True or False? In Exercises 710, determine whether the statement is true or false. If it is false, rewrite it as a true statement.When an event is almost certain to happen, its complement will be an unusual event.

Matching Probabilities In Exercises 1114, match the event with its probability. (a) 0.95 (b) 0.05 (c) 0.25 (d) 0You toss a coin and randomly select a number from 0 to 9. What is the probability of tossing tails and selecting a 3?

Matching Probabilities In Exercises 1114, match the event with its probability. (a) 0.95 (b) 0.05 (c) 0.25 (d) 0A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 153?

Matching Probabilities In Exercises 1114, match the event with its probability. (a) 0.95 (b) 0.05 (c) 0.25 (d) 0A game show contestant must randomly select a door. One door doubles her money while the other three doors leave her with no winnings. What is the probability she selects the door that doubles her money?

Matching Probabilities In Exercises 1114, match the event with its probability. (a) 0.95 (b) 0.05 (c) 0.25 (d) 0Five of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective?

Identifying a Sample Space In Exercises 1520, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriateGuessing the initial of a students middle name

Identifying a Sample Space In Exercises 1520, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate. Guessing a students letter grade (A, B, C, D, F) in a class

Identifying a Sample Space In Exercises 1520, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriateDrawing one card from a standard deck of cards

Identifying a Sample Space In Exercises 1520, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate Tossing three coins

Identifying a Sample Space In Exercises 1520, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate Determining a persons blood type (A, B, AB, O) and Rh-factor (positive, negative)

Identifying a Sample Space In Exercises 1520, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate. Rolling a pair of six-sided dice

Identifying Simple Events In Exercises 2124, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.. A computer is used to randomly select a number from 1 to 2000. Event A is selecting the number 253.

Identifying Simple Events In Exercises 2124, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.A computer is used to randomly select a number from 1 to 4000. Event B is selecting a number less than 500.

Identifying Simple Events In Exercises 2124, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning. You randomly select one card from a standard deck of 52 playing cards. Event A is selecting an ace.

Identifying Simple Events In Exercises 2124, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.You randomly select one card from a standard deck of 52 playing cards. Event B is selecting the ten of diamonds.

Using the Fundamental Counting Principle In Exercises 2528, use the Fundamental Counting Principle.Menu A restaurant offers a $12 dinner special that has 5 choices for an appetizer, 10 choices for an entre, and 4 choices for a dessert. How many different meals are available when you select an appetizer, an entre, and a dessert?

Using the Fundamental Counting Principle In Exercises 2528, use the Fundamental Counting Principle. . Laptop A laptop has 3 choices for a processor, 3 choices for a graphics card, 4 choices for memory, 6 choices for a hard drive, and 2 choices for a battery. How many ways can you customize the laptop?

Using the Fundamental Counting Principle In Exercises 2528, use the Fundamental Counting Principle. Realty A realtor uses a lock box to store the keys to a house that is for sale. The access code for the lock box consists of four digits. The first digit cannot be zero and the last digit must be even. How many different codes are available?

Using the Fundamental Counting Principle In Exercises 2528, use the Fundamental Counting Principle.True or False Quiz Assuming that no questions are left unanswered, in how many ways can a six-question true or false quiz be answered?

Finding Classical Probabilities In Exercises 2934, a probability experiment consists of rolling a 12-sided die. Find the probability of the event . Event A: rolling a 2

Finding Classical Probabilities In Exercises 2934, a probability experiment consists of rolling a 12-sided die. Find the probability of the eventEvent B: rolling a 10

Finding Classical Probabilities In Exercises 2934, a probability experiment consists of rolling a 12-sided die. Find the probability of the event Event C: rolling a number greater than 4

Finding Classical Probabilities In Exercises 2934, a probability experiment consists of rolling a 12-sided die. Find the probability of the event Event D: rolling a number less than 8

Finding Classical Probabilities In Exercises 2934, a probability experiment consists of rolling a 12-sided die. Find the probability of the event Event E: rolling a number divisible by 3

Finding Classical Probabilities In Exercises 2934, a probability experiment consists of rolling a 12-sided die. Find the probability of the event Event F: rolling a number divisible by 5

Finding Empirical Probabilities A company is conducting a survey to determine how prepared people are for a long-term power outage, natural disaster, or terrorist attack. The frequency distribution at the left shows the results. In Exercises 35 and 36, use the frequency distribution. (Adapted from Harris Interactive) What is the probability that the next person surveyed is very prepared?

Finding Empirical Probabilities A company is conducting a survey to determine how prepared people are for a long-term power outage, natural disaster, or terrorist attack. The frequency distribution at the left shows the results. In Exercises 35 and 36, use the frequency distribution. (Adapted from Harris Interactive) . . What is the probability that the next person surveyed is not too prepared?

Using a Frequency Distribution to Find Probabilities In Exercises 37 40, use the frequency distribution at the left, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the age range. (Source: U.S. Census Bureau) 18 to 20 years old

Using a Frequency Distribution to Find Probabilities In Exercises 37 40, use the frequency distribution at the left, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the age range. (Source: U.S. Census Bureau) 35 to 44 years old

Using a Frequency Distribution to Find Probabilities In Exercises 37 40, use the frequency distribution at the left, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the age range. (Source: U.S. Census Bureau) 21 to 24 years old

Using a Frequency Distribution to Find Probabilities In Exercises 37 40, use the frequency distribution at the left, which shows the number of American voters (in millions) according to age, to find the probability that a voter chosen at random is in the age range. (Source: U.S. Census Bureau) 45 to 64 years old

Classifying Types of Probability In Exercises 41 46, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning According to company records, the probability that a washing machine will need repairs during a six-year period is 0.10.

Classifying Types of Probability In Exercises 41 46, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning . The probability of choosing 6 numbers from 1 to 40 that match the 6 numbers drawn by a state lottery is 1>3,838,380 0.00000026.

Classifying Types of Probability In Exercises 41 46, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning An analyst feels that a certain stocks probability of decreasing in price over the next week is 0.75.

Classifying Types of Probability In Exercises 41 46, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning According to a survey, the probability that a voting-age citizen chosen at random is in favor of a skateboarding ban is about 0.63.

Classifying Types of Probability In Exercises 41 46, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning The probability that a randomly selected number from 1 to 100 is divisible by 6 is 0.16.

Classifying Types of Probability In Exercises 41 46, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning You think that a football teams probability of winning its next game is about 0.80.

Finding the Probability of the Complement of an Event The age distribution of the residents of San Ysidro, New Mexico, is shown at the left. In Exercises 4750, find the probability of the event. (Source: U.S. Census Bureau) Event A: randomly choosing a resident who is not 15 to 29 years old

Finding the Probability of the Complement of an Event The age distribution of the residents of San Ysidro, New Mexico, is shown at the left. In Exercises 4750, find the probability of the event. (Source: U.S. Census Bureau) Event B: randomly choosing a resident who is not 45 to 59 years old

Finding the Probability of the Complement of an Event The age distribution of the residents of San Ysidro, New Mexico, is shown at the left. In Exercises 4750, find the probability of the event. (Source: U.S. Census Bureau) Event C: randomly choosing a resident who is not 14 years old or younger

Finding the Probability of the Complement of an Event The age distribution of the residents of San Ysidro, New Mexico, is shown at the left. In Exercises 4750, find the probability of the event. (Source: U.S. Census Bureau) Event D: randomly choosing a resident who is not 75 years old or older

Probability Experiment In Exercises 5154, a probability experiment consists of rolling a six-sided die and spinning the spinner shown at the left. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the event. Then tell whether the event can be considered unusual. Event A: rolling a 5 and the spinner landing on blue

Probability Experiment In Exercises 5154, a probability experiment consists of rolling a six-sided die and spinning the spinner shown at the left. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the event. Then tell whether the event can be considered unusual. . Event B: rolling an odd number and the spinner landing on green

Probability Experiment In Exercises 5154, a probability experiment consists of rolling a six-sided die and spinning the spinner shown at the left. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the event. Then tell whether the event can be considered unusual.. Event C: rolling a number less than 6 and the spinner landing on yellow

Event D: not rolling a number less than 6 and the spinner landing on yellow

Security System The access code for a garage door consists of three digits. Each digit can be any number from 0 through 9, and each digit can be repeated. (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try?

Security System An access code consists of a letter followed by four digits. Any letter can be used, the first digit cannot be 0, and the last digit must be even. (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try?

Wet or Dry? You are planning a three-day trip to Seattle, Washington, in October. In Exercises 5760, use the tree diagram shown at the left. List the sample space.

Wet or Dry? You are planning a three-day trip to Seattle, Washington, in October. In Exercises 5760, use the tree diagram shown at the left. List the outcome(s) of the event It rains all three days.

Wet or Dry? You are planning a three-day trip to Seattle, Washington, in October. In Exercises 5760, use the tree diagram shown at the left. List the outcome(s) of the event It rains on exactly one day.

Wet or Dry? You are planning a three-day trip to Seattle, Washington, in October. In Exercises 5760, use the tree diagram shown at the left. List the outcome(s) of the event It rains on at least one day.

Graphical Analysis In Exercises 61 and 62, use the diagram. What is the probability that a registered voter in Virginia chosen at random voted in the 2012 general election?

Graphical Analysis In Exercises 61 and 62, use the diagram. What is the probability that a voter chosen at random did not vote for a Republican representative in the 2010 election?

Using a Bar Graph to Find Probabilities In Exercises 6366, use the bar graph at the left, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random isa doctorate.

Using a Bar Graph to Find Probabilities In Exercises 6366, use the bar graph at the left, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random isan associates degree

Using a Bar Graph to Find Probabilities In Exercises 6366, use the bar graph at the left, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random isa masters degree

Using a Bar Graph to Find Probabilities In Exercises 6366, use the bar graph at the left, which shows the highest level of education received by employees of a company. Find the probability that the highest level of education for an employee chosen at random isa high school diploma.

Unusual Events Can any of the events in Exercises 3740 be considered unusual? Explain.

Unusual Events Can any of the events in Exercises 6366 be considered unusual? Explain.

Genetics A Punnett square is a diagram that shows all possible gene combinations in a cross of parents whose genes are known. When two pink snapdragon flowers (RW) are crossed, there are four equally likely possible outcomes for the genetic makeup of the offspring: red (RR), pink (RW), pink (WR), and white (WW), as shown in the Punnett square at the left. When two pink snapdragons are crossed, what is the probability that the offspring will be (a) pink, (b) red, and (c) white?

Genetics There are six basic types of coloring in registered collies: sable (SSmm), tricolor (ssmm), trifactored sable (Ssmm), blue merle (ssMm), sable merle (SSMm), and trifactored sable merle (SsMm). The Punnett square below shows the possible coloring of the offspring of a trifactored sable merle collie and a trifactored sable collie. What is the probability that the offspring will have the same coloring as one of its parents?

Using a Pie Chart to Find Probabilities In Exercises 7174, use the pie chart at the left, which shows the number of workers (in thousands) by industry for the United StatesFind the probability that a worker chosen at random was employed in the services industry.

Using a Pie Chart to Find Probabilities In Exercises 7174, use the pie chart at the left, which shows the number of workers (in thousands) by industry for the United StatesFind the probability that a worker chosen at random was employed in the manufacturing industry.

Using a Pie Chart to Find Probabilities In Exercises 7174, use the pie chart at the left, which shows the number of workers (in thousands) by industry for the United StatesFind the probability that a worker chosen at random was not employed in the services industry.

Using a Pie Chart to Find Probabilities In Exercises 7174, use the pie chart at the left, which shows the number of workers (in thousands) by industry for the United StatesFind the probability that a worker chosen at random was not employed in the agriculture, forestry, fishing, and hunting industry.

College Football A stem-and-leaf plot for the numbers of touchdowns scored by all 120 NCAA Division I Football Bowl Subdivision teams is shown. Find the probability that a team chosen at random scored (a) at least 51 touchdowns, (b) between 20 and 30 touchdowns, inclusive, and (c) more than 72 touchdowns. Are any of these events unusual? Explain.

Individual Stock Price An individual stock is selected at random from the portfolio represented by the box-and-whisker plot shown. Find the probability that the stock price is (a) less than $21, (b) between $21 and $50, and (c) $30 or more.

Writing In Exercises 77 and 78, write a statement that represents the complement of the probability.The probability of randomly choosing a tea drinker who has a college degree (Assume that you are choosing from the population of all tea drinkers.)

Writing In Exercises 77 and 78, write a statement that represents the complement of the probability.The probability of randomly choosing a smoker whose mother also smoked (Assume that you are choosing from the population of all smokers.)

Rolling a Pair of Dice You roll a pair of six-sided dice and record the sum. (a) List all of the possible sums and determine the probability of rolling each sum. (b) Use technology to simulate rolling a pair of dice and record the sum 100 times. Make a tally of the 100 sums and use these results to list the probability of rolling each sum. (c) Compare the probabilities in part (a) with the probabilities in part (b). Explain any similarities or differences

Odds In Exercises 8085, use the following information. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read 2 to 3) or 2 3A beverage company puts game pieces under the caps of its drinks and claims that one in six game pieces wins a prize. The official rules of the contest state that the odds of winning a prize are 1 : 6. Is the claim one in six game pieces wins a prize correct? Explain your reasoning.

Odds In Exercises 8085, use the following information. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read 2 to 3) or 2 3The probability of winning an instant prize game is 1 10. The odds of winning a different instant prize game are 1 : 10. You want the best chance of winning. Which game should you play? Explain your reasoning.

Odds In Exercises 8085, use the following information. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read 2 to 3) or 2 3The odds of an event occurring are 4 : 5. Find (a) the probability that the event will occur and (b) the probability that the event will not occur.

Odds In Exercises 8085, use the following information. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read 2 to 3) or 2 3A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is a spade.

Odds In Exercises 8085, use the following information. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read 2 to 3) or 2 3A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is not a spade.

Odds In Exercises 8085, use the following information. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read 2 to 3) or 2 3The odds of winning an event A are p : q. Show that the probability of event A is given by P1A2 = p p + q .