The state consumers affairs office provided the following information on the frequency of

during a given year, 10 will require repairs twice, and 5 will require three or more repairs during the year. a. What is the probability that a randomly selected car will need no repairs? b. What is the probability that a randomly selected car will need at most one repair? c. What is the probability that a randomly selected car will need some repairs? 4.9 One of the games in the Texas lottery is to pay 1 to select a 3-digit number. Every Wednesday evening, the lottery commission randomly places a set of 10 balls numbered 0 –9 in each of three containers. After a complete mixing of the balls, 1 ball is selected from each container.

a. Suppose you purchase a lottery ticket. What is the probability that your 3-digit number

will be the winning number?

b. Which of the probability approaches subjective, classical, or relative frequency did

you employ in obtaining your answer in part a? 4.3 Basic Event Relations and Probability Laws 4.10 A coin is to be flipped three times. List the possible outcomes in the form result on toss 1, result on toss 2, result on toss 3.

4.11 In Exercise 4.10, assume that each one of the outcomes has probability 1

兾8 of occurring. Find the probability of

a. A: Observing exactly 1 head b. B: Observing 1 or more heads

c. C: Observing no heads 4.12 For Exercise 4.11:

a. Compute the probability of the complement of event A, event B, and event C. b. Determine whether events A and B are mutually exclusive. 4.13 A die is to be rolled and we are to observe the number that falls face up. Find the proba- bilities for these events:

a. A: Observe a 6 b. B: Observe an odd number

c. C: Observe a number greater than 3 d. D: Observe an even number and a number greater than 2

Edu. 4.14 A student has to have an accounting course and an economics course the next term. As- suming there are no schedule conflicts, describe the possible outcomes for selecting one section of the accounting course and one of the economics course if there are four possible accounting sections and three possible economics sections. Engin. 4.15 The emergency room of a hospital has two backup generators, either of which can supply enough electricity for basic hospital operations. We define events A and B as follows: event A: Generator 1 works properly event B: Generator 2 works properly Describe the following events in words:

a. Complement of A b. Either A or B

4.16 The population distribution in the United States based on raceethnicity and blood type as reported by the American Red Cross is given here. Blood Type Race Ethnicity O A B AB White 36 32.2 8.8 3.2 Black 7 2.9 2.5 .5 Asian 1.7 1.2 1 .3 All others 1.5 .8 .3 .1

a. A volunteer blood donor walks into a Red Cross Blood office. What is the probability

she will be Asian and have Type O blood? b. What is the probability that a white donor will not have Type A blood? c. What is the probability that an Asian donor will have either Type A or Type B blood? d. What is the probability that a donor will have neither Type A nor Type AB blood? 4.17 The makers of the candy MMs report that their plain MMs are composed of 15 yel- low, 10 red, 20 orange, 25 blue, 15 green, and 15 brown. Suppose you randomly select an MM, what is the probability of the following?

a. It is brown. b. It is red or green.

c. It is not blue. d. It is both red and brown.

4.4 Conditional Probability and Independence 4.18 Determine the following conditional probabilities for the events of Exercise 4.11.

a. b.

c. 4.19 Refer to Exercise 4.11. a. Are the events A and B independent? Why or why not? b. Are the events A and C independent? Why or why not? c. Are the events C and B independent? Why or why not? 4.20 Refer to Exercise 4.13. a. Which pairs of the events A B, B C, and A C are independent? Justify your answer. b. Which pairs of the events A B, B C, and A C are mutually exclusive? Justify your answer. 4.21 Refer to Exercise 4.16. Let W be the event that donor is white, B be the event donor is black, and A be the event donor is Asian. Also, let T 1 be the event donor has blood type O, T 2 be the event donor has blood type A, T 3 be the event donor has blood type B, and T 4 be the event donor has blood type AB.

a. Describe in words the event T

1 |W.

b. Compute the probability of the occurrence of the event T

1 |W, PT 1 |W.

c. Are the events W and T

1 independent? Justify your answer.

d. Are the events W and T

1 mutually exclusive? Explain your answer. 4.22 Is it possible for two events A and B to be both mutually exclusive and independent? Justify your answer. H.R. 4.23 A survey of a number of large corporations gave the following probability table for events related to the offering of a promotion involving a transfer. Married Promotion Two-Career One-Career Transfer Marriage Marriage Unmarried Total Rejected .184 .0555 .0170 .2565 Accepted .276 .3145 .1530 .7435 Total .46 .37 .17 Use the probabilities to answer the following questions:

a. What is the probability that a professional selected at random would accept the

promotion? Reject it?

b. What is the probability that a professional selected at random is part of a two-

career marriage? A one-career marriage? Soc. 4.24 A survey of workers in two manufacturing sites of a firm included the following question: How effective is management in responding to legitimate grievances of workers? The results are shown here. PB|C PA|C PA|B