2. Find Each of the Following Probabilities

MTH 155 Sample Test for Chapter 3: Statistics for Describing, Exploring, and Comparing Data and Chapter 4: Probability Dr. Claude S. Moore

1. In a statistics class, 12 students own their own computers and 9 do not. If one of the students is randomly selected, find the probability of getting one who does not own a computer.

2. Find each of the following probabilities: a. What is the probability of an event that is certain to NOT occur?

b. What is the probability of an event that is certain to occur?

c. A sample space consists of 14 separate events that are equally likely to occur. What is the probability of each?

d. On a true/false test, what is the probability of answering a question correctly if you make a random guess?

e. On a multiple-choice test with five possible answers for each question, what is the probability of answering a question correctly if you make a random guess?

3. Baseball player Mark McGwire broke a record when he hit 70 home runs in the 1998 season. During that season, he was at bat 509 times. If one of those “at bats” is randomly selected, find the probability that it is one of the times he did not hit a home run.

4. A roulette wheel has 38 slots: One slot is 0, another slot is 00, and the other slots are numbered 1 through 36. a. If you bet all of your textbook money on the number 15, what is the probability that you will win?

b. Is it “unusual” to win when you bet on a single number in roulette? Why? 5. In a Bruskin-Goldring Research poll, respondents were asked how a fruitcake should be used. One hundred forty-five respondents indicated that it should be used for a doorstop, and 800 other respondents cited other uses, including birdfeed, landfill, and a gift. If one of these respondents is randomly selected, what is the probability of getting someone who would use the fruitcake as a doorstop?

6. Find each of the following probabilities: a. If P( A ) = 0.731, find P(A).

b. Based on data from the National Health Examination, the probability of a randomly selected adult male being 6 ft or shorter is 0.86. Find the probability of randomly selecting an adult male and getting someone taller than 6 ft.

7. In a study of 82 young (under the age of 32) drivers, 39 were men who were ticketed, 11 were men who were not ticketed, 8 were women who were ticketed, and 24 were women who were not ticketed (based on data from the Department of Transportation). If one of these subjects is randomly selected, find the probability of getting a man or someone who was ticketed.

8. Determine whether the following events are mutually exclusive: a. If P(A) = 4/15, P(B) = 7/15, and P(A or B) = 10/15, what do you know about events A and B?

b. If P(A) = 2/ 7, P(B) = 4/ 7, and P(A or B) = 6/ 7, what do you know about events A and B?

9. A pool of potential jurors consists of 10 men and 12 women. If two different people are randomly selected from this pool, find the probability that they are both women. 10. A quick quiz consists of five multiple-choice questions, each with four possible answers, only one of which is correct. If you make random guesses for each answer, what is the probability that all five of your answers are wrong?

11. A classic excuse for a missed test is offered by four students who claim that their car had a flat tire. On the makeup test, the instructor asks the students to identify the particular tire that went flat. If they really didn’t have a flat tire and randomly select one that supposedly went flat, what if the probability that they will all select the same tire?

12. Does P(x) = x/6 (where x can take on the values of 0, 1, 2, 3) describe a probability distribution? Explain your answer.

13. To settle a paternity suit, two different people are given blood tests. If x is the number having group A blood, then x can be 0, 1, or 2, and the corresponding probabilities are 0.36, 0.48, and 0.16, respectively (based on data from the Greater New York Blood Program). Determine whether the above information describes a probability distribution. If it does not, explain why. If it does, find its mean.

14. When you give a casino $10 for a bet on the “pass line” in the game of craps, there is a 244/495 probability that you will win $10 and a 251/495 probability that you will lose $10. What is your expected value? 15. Given that n = 6 and p = 0.95 (in a binomial probability distribution), find the following probabilities: a. The probability of exactly 2 successes.

b. The probability of at least 2 successes.

16. The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80% of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. a. Find the probability that exactly 8 flights arrive on time.

b. Would it be unusual for Southwest to have 6 flights arrive late? Why or why not? 17. Several students are unprepared for a multiple-choice test with 20 questions, and all of their answers are guesses. Each question has four possible answers, and only one of them is correct. a. Find the mean for the number of correct answers for such students.

b. Find the standard deviation for the number of correct answers for such students.

c. Would it be unusual for a student to pass by guessing and getting at least 12 correct answers? Why or why not?

18. Mars, Inc., claims that 10% of its M&M plain candies are blue, and a sample of 150 such candies is randomly selected. a. Find the mean for the number of blue candies in such groups of 150. b. Find the standard deviation for the number of blue candies in such groups of 150.

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