Solved: College Courses At a large university, the

State which events are independent and which are dependent. a. Tossing a coin and drawing a card from a deck Independent b. Drawing a ball from an urn, not replacing it, and then drawing a second ball Dependent c. Getting a raise in salary and purchasing a new car Dependent d. Driving on ice and having an accident Dependent e. Having a large shoe size and having a high IQ Independent f. A father being left-handed and a daughter being left-handed Dependent g. Smoking excessively and having lung cancer Dependent h. Eating an excessive amount of ice cream and smoking an excessive amount of cigarettes Independent

Exercise If 37% of high school students said that they exercise regularly, find the probability that 5 randomly selected high school students will say that they exercise regularly.Would you consider this event likely or unlikely to occur? Explain your answer. 0.007; the event is very unlikely to occur since its probability is very small.

Video and Computer Games Sixty-nine percent of U.S. heads of households play video or computer games. Choose 4 heads of households at random. Find the probability that a. None play video or computer games 0.009 b. All four do 0.227 Source: www.theesa.com

Seat Belt Use The Gallup Poll reported that 52% of Americans used a seat belt the last time they got into a car. If 4 people are selected at random, find the probability that they all used a seat belt the last time they got into a car. 7.3% Source: 100% American.

Automobile Sales An automobile salesperson finds the probability of making a sale is 0.21. If she talks to 4 customers, find the probability that she will make 4 sales. Is the event likely or unlikely to occur? Explain your answer. 0.00194 The event is highly unlikely since the probability is small.

Prison Populations If 25% of U.S. federal prison inmates are not U.S. citizens, find the probability that 2 randomly selected federal prison inmates will not be U.S. citizens. 6.3% Source: Harpers Index.

MLS Players Of the 216 players on major league soccer rosters, 80.1% are U.S. citizens. If 3 players are selected at random for an exhibition, what is the probability that all are U.S. citizens? 0.5139 Source: USA Today.

Working Women and Computer Use It is reported that 72% of working women use computers at work. Choose 5 working women at random. Find a. The probability that at least 1 doesnt use a computer at work 0.807 b. The probability that all 5 use a computer in their jobs 0.194 Source: www.infoplease.com

Text Messages via Cell Phones Thirty-five percent of people who own cell phones use their phones to send and receive text messages. Choose 4 cell phone owners at random. What is the probability that none use their phones for texting? 0.179

Cards If 2 cards are selected from a standard deck of 52 cards without replacement, find these probabilities. a. Both are spades. b. Both are the same suit. c. Both are kings.

Cable Television In 2006, 86% of U.S. households had cable TV. Choose 3 households at random. Find the probability that a. None of the 3 households had cable TV 0.003 b. All 3 households had cable TV 0.636 c. At least 1 of the 3 households had cable TV 0.997 Source: www.infoplease.com

Flashlight Batteries Aflashlight has 6 batteries, 2 of which are defective. If 2 are selected at random without replacement, find the probability that both are defective. 1 15 1 221 4 17 1 17

Drawing a Card Four cards are drawn from a deck without replacement. Find these probabilities. a. All are kings. b. All are diamonds. c. All are red cards.

Scientific Study In a scientific study there are 8 guinea pigs, 5 of which are pregnant. If 3 are selected at random without replacement, find the probability that all are pregnant.

In Exercise 14, find the probability that none are pregnant.

Winning a Door Prize At a gathering consisting of 10 men and 20 women, two door prizes are awarded. Find the probability that both prizes are won by men. The winning ticket is not replaced. Would you consider this event likely or unlikely to occur? unlikely

In Exercise 16, find the probability that both prizes are won by women. Which event (Exercise 16 or 17) is most likely to occur?

Sales A manufacturer makes two models of an item: model I, which accounts for 80% of unit sales, and model II, which accounts for 20% of unit sales. Because of defects, the manufacturer has to replace (or exchange) 10% of its model I and 18% of its model II. If a model is selected at random, find the probability that it will be defective.

Student Financial Aid In a recent year 8,073,000 male students and 10,980,000 female students were enrolled as undergraduates. Receiving aid were 60.6% of the male students and 65.2% of the female students. Of those receiving aid, 44.8% of the males got federal aid and 50.4% of the females got federal aid. Choose 1 student at random. (Hint: Make a tree diagram.) Find the probability that the student is a. A male student without aid 0.167 b. A male student, given that the student has aid 0.406 c. A female student or a student who receives federal aid 0.691 Source: www.nces.gov

Selecting Colored Balls Urn 1 contains 5 red balls and 3 black balls. Urn 2 contains 3 red balls and 1 black ball. Urn 3 contains 4 red balls and 2 black balls. If an urn is selected at random and a ball is drawn, find the probability it will be red.

Automobile Insurance An insurance company classifies drivers as low-risk, medium-risk, and highrisk. Of those insured, 60% are low-risk, 30% are medium-risk, and 10% are high-risk. After a study, the company finds that during a 1-year period, 1% of the low-risk drivers had an accident, 5% of the medium-risk drivers had an accident, and 9% of the high-risk drivers had an accident. If a driver is selected at random, find the probability that the driver will have had an accident during the year. 0.03

Defective Items A production process produces an item. On average, 15% of all items produced are defective. Each item is inspected before being shipped, and the inspector misclassifies an item 10% of the time. What proportion of the items will be classified as good? What is the probability that an item is defective given that it was classified as good? 0.78 0.0192

Prison Populations For a recent year, 0.99 of the incarcerated population is adults and 0.07 of these are female. If an incarcerated person is selected at random, find the probability that the person is a female given that the person is an adult. 0.071 Source: Bureau of Justice.

Rolling Dice Roll two standard dice and add the numbers. What is the probability of getting a number larger than 9 for the first time on the third roll? 0.1157

Model Railroad Circuit A circuit to run a model railroad has 8 switches. Two are defective. If you select 2 switches at random and test them, find the probability that the second one is defective, given that the first one is defective.

Country Club Activities At the Avonlea Country Club, 73% of the members play bridge and swim, and 82% play bridge. If a member is selected at random, find the probability that the member swims, given that the member plays bridge. 89%

College Courses At a large university, the probability that a student takes calculus and is on the deans list is 0.042. The probability that a student is on the deans list is 0.21. Find the probability that the student is taking calculus, given that he or she is on the deans list. 0.2

Country Club Members At the Coulterville Country Club, 72% of the members play golf and are college graduates, and 80% of the members play golf. If a member is selected at random, find the probability that the member is a college graduate given that the member plays golf. 0.9

Pizza and Salads In a pizza restaurant, 95% of the customers order pizza. If 65% of the customers order pizza and a salad, find the probability that a customer who orders pizza will also order a salad. 68.4%

Gift Baskets The Gift Basket Store had the following premade gift baskets containing the following combinations in stock. 17 Cookies Mugs Candy Coffee 20 13 10 Tea 12 10 12 Choose 1 basket at random. Find the probability that it contains a. Coffee or candy 0.7143 b. Tea given that it contains mugs 0.4348 c. Tea and cookies 0.1558 Source: www.infoplease.com

Blood Types and Rh Factors In addition to being grouped into four types, human blood is grouped by its Rhesus (Rh) factor. Consider the figures below which show the distributions of these groups for Americans. Choose 1 American at random. Find the probability that the person a. Is a universal donor, i.e., has O negative blood b. Has type O blood given that the person is Rh+ c. Has A+ or AB blood d. Has Rh- given that the person has type B Source: www.infoplease.com

Doctor Specialties Below are listed the numbers of doctors in various specialties by gender. Choose 1 doctor at random. a. Find P (malepediatrician). b. Find P (pathologist|female). c. Are the characteristics “female” and “pathologist” independent? Explain. Source: World Almanac.

Olympic Medals The medal distribution from the 2008 Summer Olympic Games for the top 23 countries is shown below. Gold Silver Bronze United States 36 38 36 Russia 23 21 28 China 51 21 28 Great Britain 19 13 15 Others 173 209 246 Choose 1 medal winner at random. a. Find the probability that the winner won the gold medal, given that the winner was from the United States. 0.327 b. Find the probability that the winner was from the United States, given that she or he won a gold medal. 0.119 c. Are the events medal winner is from United States and gold medal won independent? Explain. No. P(G_U.S.) _ P(G)

Computer Ownership At a local university 54.3% of incoming first-year students have computers. If 3 students are selected at random, find the following probabilities. a. None have computers. 0.0954 b. At least one has a computer. 0.9046 c. All have computers. 0.1601

Leisure Time Exercise Only 27% of U.S. adults get enough leisure time exercise to achieve cardiovascular fitness. Choose 3 adults at random. Find the probability that a. All 3 get enough daily exercise 0.0197 b. At least 1 of the 3 gets enough exercise 0.611 Source: www.infoplease.com

Customer Purchases In a department store there are 120 customers, 90 of whom will buy at least 1 item. If 5 customers are selected at random, one by one, find the probability that all will buy at least 1 item. 0.231

Marital Status of Women According to the Statistical Abstract of the United States, 70.3% of females ages 20 to 24 have never been married. Choose 5 young women in this age category at random. Find the probability that a. None has ever been married 0.1717 b. At least 1 has been married 0.8283 Source: New York Times Almanac.

Fatal Accidents The American Automobile Association (AAA) reports that of the fatal car and truck accidents, 54% are caused by car driver error. If 3 accidents are chosen at random, find the probability that a. All are caused by car driver error 0.157 b. None is caused by car driver error 0.097 c. At least 1 is caused by car driver error 0.903 Source: AAA quoted on CNN.

On-Time Airplane Arrivals The greater Cincinnati airport led major U.S. airports in on-time arrivals in the last quarter of 2005 with an 84.3% on-time rate. Choose 5 arrivals at random and find the probability that at least 1 was not on time. 0.574 Source: www.census.gov

Online Electronic Games Fifty-six percent of electronic gamers play games online, and sixty-four percent of those gamers are female. What is the probability that a randomly selected gamer plays games online and is male?

Reading to Children Fifty-eight percent of American children (ages 3 to 5) are read to every day by someone at home. Suppose 5 children are randomly selected. What is the probability that at least 1 is read to every day by someone at home? 0.9869 Source: Federal Interagency Forum on Child and Family Statistics.

Doctoral Assistantships Of Ph.D. students, 60% have paid assistantships. If 3 students are selected at random, find the probabilities a. All have assistantships 0.216 b. None has an assistantship 0.064 c. At least 1 has an assistantship 0.936 Source: U.S. Department of Education, Chronicle of Higher Education.

Selecting Cards If 4 cards are drawn from a deck of 52 and not replaced, find the probability of getting at least 1 club.

Full-Time College Enrollment The majority (69%) of undergraduate students were enrolled in a 4-year college in a recent year. Eighty-one percent of those enrolled attended full-time. Choose 1 enrolled undergraduate student at random. What is the probability that she or he is a part-time student at a 4-year college? 0.131 Source: www.census.gov

Family and Childrens Computer Games It was reported that 19.8% of computer games sold in 2005 were classified as family and childrens. Choose 5 purchased computer games at random. Find the probability that a. None of the 5 was family and childrens 0.332 b. At least 1 of the 5 was family and childrens 0.668 Source: www.theesa.com

Medication Effectiveness A medication is 75% effective against a bacterial infection. Find the probability that if 12 people take the medication, at least 1 persons infection will not improve. 96.8%

Tossing a Coin Acoin is tossed 5 times; find the probability of getting at least 1 tail.Would you consider this event likely to happen? Explain your answer.

Selecting a Letter of the Alphabet If 3 letters of the alphabet are selected at random, find the probability of getting at least 1 letter x. Letters can be used more than once. Would you consider this event likely to happen? Explain your answer. 0.111; the event is very unlikely to occur since the probability is only about 11%.

Rolling a Die A die is rolled 6 times. Find the probability of getting at least one 4. Would you consider this event likely or unlikely? Explain your answer. 0.665 It will happen almost 67% of the time. Its somewhat likely.

High School Grades of First-Year College Students Forty-seven percent of first-year college students enrolled in 2005 had an average grade of A in high school compared to 20% of first-year college students in 1970. Choose 6 first-year college students at random enrolled in 2005. Find the probability that a. All had an A average in high school 0.011 b. None had an A average in high school 0.022 c. At least 1 had an A average in high school 0.978 Source: www.census.gov

Rolling a Die If a die is rolled 3 times, find the probability of getting at least 1 even number.

Selecting a Flower In a large vase, there are 8 roses, 5 daisies, 12 lilies, and 9 orchids. If 4 flowers are selected at random, find the probability that at least 1 of the flowers is a rose. Would you consider this event likely to occur? Explain your answer. 0.678; yes the event is a little more likely to occur than not since the probability is about 68%.

Let A and B be two mutually exclusive events. Are A and B independent events? Explain your answer. No, since P(A _ B) _ 0 and does not equal P(A) _ P(B).

Types of Vehicles The Bargain Auto Mall has the following cars in stock. SUV Compact Mid-sized Foreign 20 50 20 Domestic 65 100 45 Are the events compact and domestic independent? Explain. No, since P(C_D) _ P(C).

College Enrollment An admissions director knows that the probability a student will enroll after a campus visit is 0.55, or P(E)=0.55. While students are on campus visits, interviews with professors are arranged. The admissions director computes these conditional probabilities for students enrolling after visiting three professors, DW, LP, and MH. P(E|DW)=0.95 P(E|LP)=0.55 P(E|MH)=0.15 Is there something wrong with the numbers? Explain.

Commercials Event A is the event that a person remembers a certain product commercial. Event B is the event that a person buys the product. If P(B) _ 0.35, comment on each of these conditional probabilities if you were vice president for sales. a. P(B_A) _ 0.20 b. P(B_A) _ 0.35 c. P(B_A) _ 0.553