Solution: Using Probability to Identify Unlikely Events. In Exercises 2936, consider an

Florida Lottery Let A denote the event of placing a $1 straight bet on the Florida Play 4 lottery and winning. The chance of event A occurring is 1 in 10,000. What is the value of P(A)? What is the value of P ( A ) ?

Probability Given that the following statement is incorrect, rewrite it correctly: The probability of a baby being born a boy is 5050.

Interpreting Weather While this exercise was being created, Weather.com indicated that there was a 20% chance of rain for the author's home region. Based on that report, which of the following is the most reasonable interpretation? a. 1/5 of the author's region will get rain today. b. In the author's region, it will rain for 1/5 of the day. c. In the author's region, there is a 1/5 probability that it will rain at some point during the day.

Subjective Probability Estimate the probability that the next time you ride in a car, you will not be delayed because of some car crash blocking the road.

Identifying Probability Values Which of the following values are not probabilities? 5:2 3/7 7/3 0.9 0.123 123/456 456/123 0 1

U.S. President Who was the 14th president of the United States: Taylor, Fillmore, Pierce, or Buchanan? If you make a random guess for the answer to that question, what is the probability that your answer is the correct answer of Pierce?

Digits of Pi Which of the following is the mean of the first 100 digits of pi after the decimal point: 4.4, 4.5, 4.6, 4.7, or 4.8? If you make a random guess for the answer to that question, what is the probability that your answer is the correct answer of 4.8?

The Die Is Cast When rolling a single die, what is the probability that the outcome is 7?

In Exercises 912, assume that 400 births are randomly selected. Use subjective judgment to determine whether the given outcome is unlikely, and also determine whether it is unusual in the sense that the result is far from what is typically expected Exactly 205 girls

In Exercises 912, assume that 400 births are randomly selected. Use subjective judgment to determine whether the given outcome is unlikely, and also determine whether it is unusual in the sense that the result is far from what is typically expected Exactly 380 girls.

In Exercises 912, assume that 400 births are randomly selected. Use subjective judgment to determine whether the given outcome is unlikely, and also determine whether it is unusual in the sense that the result is far from what is typically expected Exactly 111 girls

In Exercises 912, assume that 400 births are randomly selected. Use subjective judgment to determine whether the given outcome is unlikely, and also determine whether it is unusual in the sense that the result is far from what is typically expected Exactly 197 girls.

In Exercises 1320, express the indicated degree of likelihood as a probability value between 0 and 1. Traffic Light When arriving at the traffic light closest to the author's home, there is a 25% chance that the light will be red

In Exercises 1320, express the indicated degree of likelihood as a probability value between 0 and 1.Weather While this exercise was being created, Weather.com indicated that there is a 20% chance of rain for the author's home region.

In Exercises 1320, express the indicated degree of likelihood as a probability value between 0 and 1.Testing If you make a random guess for the answer to a true/false test question, there is a 5050 chance of being correct.

In Exercises 1320, express the indicated degree of likelihood as a probability value between 0 and 1.Pierced Ears Based on a Harris poll, there is a 5050 chance that a randomly selected adult has pierced ears.

In Exercises 1320, express the indicated degree of likelihood as a probability value between 0 and 1.SAT Test When guessing the answer to a multiplechoice question on an SAT test, the chance of guessing correctly is 1 in 5.

In Exercises 1320, express the indicated degree of likelihood as a probability value between 0 and 1.. Dice When rolling a pair of dice at the Bellagio Casino in Las Vegas, there is 1 chance in 36 that the outcome is a 12.

In Exercises 1320, express the indicated degree of likelihood as a probability value between 0 and 1. Statistics Test It is impossible to pass a statistics test without studying.

In Exercises 1320, express the indicated degree of likelihood as a probability value between 0 and 1.Death and Taxes Benjamin Franklin said that death is a certainty of life.

In Exercises 2124, refer to the sample data in Table 41, which is included with the Chapter Problem. Assume that one of the subjects included in Table 41 is randomly selected.PreEmployment Drug Screening Find the probability of selecting someone who got a result that is a false negative. Who would suffer from a false negative result? Why?

In Exercises 2124, refer to the sample data in Table 41, which is included with the Chapter Problem. Assume that one of the subjects included in Table 41 is randomly selected.PreEmployment Drug Screening Find the probability of selecting someone who got a result that is a false positive. Who would suffer from a false positive result? Why?

In Exercises 2124, refer to the sample data in Table 41, which is included with the Chapter Problem. Assume that one of the subjects included in Table 41 is randomly selected. PreEmployment Drug Screening Find the probability of selecting someone who uses drugs. Is the result close to the probability of 0.134 for a positive test result?

In Exercises 2124, refer to the sample data in Table 41, which is included with the Chapter Problem. Assume that one of the subjects included in Table 41 is randomly selected.PreEmployment Drug Screening Find the probability of selecting someone who does not use drugs. Is the result close to the probability of 0.866 for a negative test result?

XSORT Gender Selection MicroSort's XSORT genderselection technique is designed to increase the likelihood that a baby will be a girl. In updated results (as of this writing) of the XSORT genderselection technique, 945 births consisted of 879 baby girls and 66 baby boys (based on data from the Genetics & IVF Institute). Based on these results, what is the probability of a girl born to a couple using MicroSort's XSORT method? Does it appear that the technique is effective in increasing the likelihood that a baby will be a girl?

YSORT Gender Selection MicroSort's YSORT genderselection technique is designed to increase the likelihood that a baby will be a boy. In updated results (as of this writing) from a test of MicroSort's YSORT genderselection technique, 291 births consisted of 239 baby boys and 52 baby girls (based on data from the Genetics & IVF Institute). Based on these results, what is the probability of a boy born to a couple using MicroSort's YSORT method? Does it appear that the technique is effective in increasing the likelihood that a baby will be a boy?

Struck by Lightning In a recent year, 304 of the approximately 300,000,000 people in the United States were struck by lightning. Estimate the probability that a randomly selected person in the United States will be struck by lightning this year. Is a golfer reasoning correctly if he or she is caught out in a thunderstorm and does not seek shelter from lightning because the probability of being struck is so small?

Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the expected value of 3/4, as claimed by Mendel?

Using Probability to Identify Unlikely Events. In Exercises 2936, consider an event to be unlikely if its probability is less than or equal to 0.05. (This is equivalent to the same criterion commonly used in inferential statistics, but the value of 0.05 is not absolutely rigid, and other values such as 0.01 are sometimes used instead.)Guessing Birthdays On their first date, Kelly asks Mike to guess the date of her birth, not including the year. a. What is the probability that Mike will guess correctly? (Ignore leap years.) b. Would it be unlikely for him to guess correctly on his first try? c. If you were Kelly, and Mike did guess correctly on his first try, would you believe his claim that he made a lucky guess, or would you be convinced that he already knew when you were born? d. If Kelly asks Mike to guess her age, and Mike's guess is too high by 15 years, what is the probability that Mike and Kelly will have a second date?

Using Probability to Identify Unlikely Events. In Exercises 2936, consider an event to be unlikely if its probability is less than or equal to 0.05. (This is equivalent to the same criterion commonly used in inferential statistics, but the value of 0.05 is not absolutely rigid, and other values such as 0.01 are sometimes used instead.)Credit Card Purchases In a survey, 169 respondents say that they never use a credit card, 1227 say that they use it sometimes, and 2834 say that they use it frequently. What is the probability that a randomly selected person uses a credit card frequently? Is it unlikely for someone to use a credit card frequently? How are all of these results affected by the fact that the responses were obtained by those who decided to respond to the survey posted on the Internet by America OnLine?

Car Crashes In a recent year, among 135,933,000 registered passenger cars in the United States, there were 10,427,000 crashes. Find the probability that a randomly selected passenger car in the United States will crash this year. Is it unlikely for a car to crash in a given year? What does this suggest about driving?

Using Probability to Identify Unlikely Events. In Exercises 2936, consider an event to be unlikely if its probability is less than or equal to 0.05. (This is equivalent to the same criterion commonly used in inferential statistics, but the value of 0.05 is not absolutely rigid, and other values such as 0.01 are sometimes used instead.)Air Travel Fatalities One measure of air travel safety is this: There are 117 fatalities per billion passenger flights. Express that measure as a probability. Is it unlikely for an air passenger to be a fatality? How does air travel compare to the car fatality rate of 40 fatalities per billion trips? Is this comparison fair?

Using Probability to Identify Unlikely Events. In Exercises 2936, consider an event to be unlikely if its probability is less than or equal to 0.05. (This is equivalent to the same criterion commonly used in inferential statistics, but the value of 0.05 is not absolutely rigid, and other values such as 0.01 are sometimes used instead.)Texting While Driving In a New York Times/CBS News poll, respondents were asked if it should be legal or illegal to send a text message while driving. Eight said that it should be legal and 804 said that it should be illegal. What is the probability of randomly selecting someone who believes it should be legal to text while driving? Is it unlikely to randomly select someone with that belief?

Using Probability to Identify Unlikely Events. In Exercises 2936, consider an event to be unlikely if its probability is less than or equal to 0.05. (This is equivalent to the same criterion commonly used in inferential statistics, but the value of 0.05 is not absolutely rigid, and other values such as 0.01 are sometimes used instead.)Cell Phones While Driving In a New York Times/CBS News poll, respondents were asked if it should be legal or illegal to use handheld cell phones while driving. One hundred fortyone said that it should be legal, and 663 said that it should be illegal. What is the probability of randomly selecting someone who believes it should be legal to use a handheld cell phone while driving? Is it unlikely to randomly select someone with that belief?

Using Probability to Identify Unlikely Events. In Exercises 2936, consider an event to be unlikely if its probability is less than or equal to 0.05. (This is equivalent to the same criterion commonly used in inferential statistics, but the value of 0.05 is not absolutely rigid, and other values such as 0.01 are sometimes used instead.)Favorite Seat on a Plane Among respondents asked which is their favorite seat on a plane, 492 chose the window seat, 8 chose the middle seat, and 306 chose the aisle seat (based on data from USA Today). What is the probability that a passenger prefers the middle seat? Is is unlikely for a passenger to prefer the middle seat? If so, why do you think the middle seat is so unpopular?

Using Probability to Identify Unlikely Events. In Exercises 2936, consider an event to be unlikely if its probability is less than or equal to 0.05. (This is equivalent to the same criterion commonly used in inferential statistics, but the value of 0.05 is not absolutely rigid, and other values such as 0.01 are sometimes used instead.)At the End of the Day In a Marist poll, respondents chose the most annoying phrases used in conversation. Nineteen chose at the end of the day, 441 chose whatever, 235 chose you know, 103 chose it is what it is, 66 chose anyway, and 75 were unsure. Based on these results, what is the probability of selecting someone who considers at the end of the day to be the most annoying phrase? At the end of the day, is it unlikely to select someone with that choice?

Probability from a Sample Space. In Exercises 3742, use the given sample space or construct the required sample space to find the indicated probabilityThree Children Use this sample space listing the eight simple events that are possible when a couple has three children (as in Example 1): {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there is exactly one girl.

Probability from a Sample Space. In Exercises 3742, use the given sample space or construct the required sample space to find the indicated probability Three Children Using the same sample space and assumption from Exercise 37, find the probability that when a couple has three children, there are exactly two girls.

Probability from a Sample Space. In Exercises 3742, use the given sample space or construct the required sample space to find the indicated probabilityTwo Children Exercise 37 lists the sample space for a couple having three children. First identify the sample space for a couple having two children, then find the probability of getting one child of each gender. Again assume that boys and girls are equally likely.

Probability from a Sample Space. In Exercises 3742, use the given sample space or construct the required sample space to find the indicated probability Four Children Exercise 37 lists the sample space for a couple having three children. First identify the sample space for a couple having four children, then find the probability of getting three girls and one boy (in any order).

Probability from a Sample Space. In Exercises 3742, use the given sample space or construct the required sample space to find the indicated probability. Genetics: Eye Color Each of two parents has the genotype brown/blue, which consists of the pair of alleles that determine eye color, and each parent contributes one of those alleles to a child. Assume that if the child has at least one brown allele, that color will dominate and the eyes will be brown. (The actual determination of eye color is somewhat more complicated.) a. List the different possible outcomes. Assume that these outcomes are equally likely. b. What is the probability that a child of these parents will have the blue/blue genotype? c. What is the probability that the child will have brown eyes?

Probability from a Sample Space. In Exercises 3742, use the given sample space or construct the required sample space to find the indicated probabilityXLinked Genetic Disease Men have XY (or YX) chromosomes and women have XX chromosomes. Xlinked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is good. In the following, represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child.a. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a son will inherit the disease? b. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a daughter will inherit the disease? c. If a mother has one defective x chromosome and one good X chromosome and the father has good XY chromosomes, what is the probability that a son will inherit the disease? d. If a mother has one defective x chromosome and one good X chromosome and the father has good XY chromosomes, what is the probability that a daughter will inherit the disease?

Odds. In Exercises 4346, answer the given questions that involve odds.. Texas Pick 3 In the Texas Pick 3 lottery, you can bet $1 by selecting the exact order of three digits between 0 and 9 inclusive, so the probability of winning is 1/1000. If the same three numbers are drawn in the same order, you collect $500, so your net profit is $499. a. Find the actual odds against winning. b. Find the payoff odds. c. The web site www.txlottery.org indicates Odds 1:1000 for this bet. Is that description accurate?

Odds. In Exercises 4346, answer the given questions that involve odds.Finding Odds in Roulette A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You place a bet that the outcome is an odd number. a. What is your probability of winning? b. What are the actual odds against winning? c. When you bet that the outcome is an odd number, the payoff odds are 1:1. How much profit do you make if you bet $18 and win? d. How much profit would you make on the $18 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning? (Recommendation: Don't actually try to convince any casino of this their sense of humor is remarkably absent when it comes to things of this sort.)

Odds. In Exercises 4346, answer the given questions that involve odds. Kentucky Derby Odds When the horse Super Saver won the 136th Kentucky Derby, a $2 bet that Super Saver would win resulted in a return of $18. a. How much net profit was made from a $2 win bet on Super Saver? b. What were the payoff odds against a Super Saver win? c. Based on preliminary wagering before the race, bettors collectively believed that Super Saver had a 0.093 probability of winning. Assuming that 0.093 was the true probability of a Super Saver victory, what were the actual odds against his winning? d. If the payoff odds were the actual odds found in part (c), how much would a $2 win ticket be worth after the Super Saver win?

Odds. In Exercises 4346, answer the given questions that involve odds.Finding Probability from Odds If the actual odds against event A are a:b, then P ( A ) = b / ( a + b ) . Find the probability of the horse Make Music for Me winning the 136th Kentucky Derby, given that the actual odds against his winning that race were 36:1.

Relative Risk and Odds Ratio In a clinical trial of 2103 subjects treated with Nasonex, 26 reported headaches. In a control group of 1671 subjects given a placebo, 22 reported headaches. Denoting the proportion of headaches in the treatment group by p t and denoting the proportion of headaches in the control (placebo) group by p c , the relative risk is p t / p c . The relative risk is a measure of the strength of the effect of the Nasonex treatment. Another such measure is the odds ratio, which is the ratio of the odds in favor of a headache for the treatment group to the odds in favor of a headache for the control (placebo) group, found by evaluating the following: p t / ( 1 p t ) p c / ( 1 p c ) The relative risk and odds ratios are commonly used in medicine and epidemiological studies. Find the relative risk and odds ratio for the headache data. What do the results suggest about the risk of a headache from the Nasonex treatment?

Flies on an Orange If two flies land on an orange, find the probability that they are on points that are within the same hemisphere.

Points on a Stick Two points along a straight stick are randomly selected. The stick is then broken at those two points. Find the probability that the three resulting pieces can be arranged to form a triangle. (This is possibly the most difficult exercise in this book.) Proportions of Males/Females