Fundamentals of Probability and Statistics for Engineers

2.19 A rifle is fired at a target. Assuming that the probability of scoring a hit is 0.9 for
each shot and that the shots are independent, compute the probability that, in
order to score a hit:
(a) It takes more than two shots.
(b) The number of shots required is between four and six (inclusive).

2.20 Events A and B are mutually exclusive. Can they also be independent? Explain.

2.21 Let
(a) A and B are independent?
(b) A and B are mutually exclusive?

2.22 Let Is it possible to determine P(A) and P(B)?
Answer the same question if, in addition:
(a) A and B are independent.
(b) A and B are mutually exclusive.

a b

A

B

C

0.90

0.90

0.85

Figure 2.12 Figure for Problem 2.18(a)

a b

A B

CD

pA

pC pD

pB

Figure 2.13 Figure for Problem 2.18(b)

32 Fundamentals of Probability and Statistics for Engineers

P A)ˆ 0 :4, andP A[B)ˆ 0 :7. What isP B) if:

P A[B)ˆ 0 :75, andP AB)ˆ 0 :25.