If a six sided die is tossed two times, the probability of obtaining two "4s" in a row is

ASSIGNMENT #3

1. The collection of all possible sample points in an experiment is

a.

the sample space

b.

a sample point

c.

an experiment

d.

the population

2. From a group of six people, two individuals are to be selected at random. How many possible selections are there?

a.

12

b.

36

c.

15

d.

8

3. Two events, A and B, are mutually exclusive and each have a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is

a.

one

b.

any positive value

c.

zero

d.

any value between 0 and 1

4. If A and B are independent events with P(A) = 0.65 and P(A ∩ B) = 0.26, then, P(B) =

a.

0.400

b.

0.169

c.

0.390

d.

0.650

5. If P(A) = 0.4, P(B | A) = 0.35, P(A  B) = 0.69, then P(B) =

a.

0.14

b.

0.43

c.

0.75

d.

0.59

6. Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is

a.

much larger than one

b.

zero

c.

infinity

d.

none of these alternatives is correct

7. Assume your favorite football team has 2 games left to finish the season. The outcome of each game can be win, lose or tie. The number of possible outcomes is

a.

2

b.

4

c.

6

d.

9

8. If a coin is tossed three times, the likelihood of obtaining three heads in a row is

a.

0.000

b.

0.500

c.

0.875

d.

0.125

9. If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A ∩ B) =

a.

0.76

b.

1.00

c.

0.24

d.

0.20

10. An automobile dealer has kept records on the customers who visited his showroom. 40% of the people who visited his dealership were female. Furthermore, his records show that 35% of the females who visited his dealership purchased an automobile, while 20% of the males who visited his dealership purchased an automobile. Given that an automobile is purchased at the dealership, what is the probability that the customer is a female?

a.

0.080

b.

0.550

c.

0.400

d.

0.538

11. A bank gives a test to screen prospective employees. Among those who perform their jobs satisfactorily, 65% pass the test. Among those who do not perform satisfactorily, 25% pass the test. According to the bank’s records, 90% of its employees perform their jobs satisfactorily. What is the probability that a prospective employee who passed the test will not perform satisfactorily?

a.

0.028

b.

0.041

c.

0.025

d.

0.585

12. How many committees consisting of 3 female and 5 male students can be selected from a group of 5 female and 8 male students?

a.

200

b.

20,160

c.

396

d.

560

e.

66

13. Consider the experiment of tossing a coin three times and recording the outcome. Compute the total number of possible outcomes. You might also want to list the possible outcomes – this will help you with the next several problems.

a.

4

b.

8

c.

6

d.

10

14. Refer to question 13. Define an event A = {HHH, TTT, HTH} and an event B = {HHH, HTH, HHT, TTH}. Compute P(A) and P(B).

a.

P(A) = 3/8; P(B) = 1/2

b.

P(A) = 1/2; P(B) = 1/2

c.

P(A) = 3/4; P(B) = 1/2

d.

P(A) = 1/4; P(B) = 1/4

15. Refer to question 14. Compute P(AB).

a.

1/4

b.

1/2

c.

3/4

d.

5/8

e.

1

16. Refer to question 14. Compute P(BA).

a.

1/4

b.

1/3

c.

2/3

d.

3/4

e.

1

17. Refer to question 14. Are events A and B independent?

a.

yes

b.

no

18. Refer to question 14. Are events A and B mutually exclusive?

a.

yes

b.

no

19. If a six-sided die is tossed two times, the probability of obtaining two "4s" in a row is

a.

1/6

b.

1/36

c.

1/96

d.

1/216

20. Events A and B are mutually exclusive. Which of the following statements is also true?

a.

A and B are also independent.

b.

P(A  B) = P(A)P(B)

c.

P(A  B) = P(A) + P(B)

d.

P(A ∩ B) = P(A) + P(B)

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