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) 0 :4, andP A[B) 0 :7. What isP B) if:
P A[B) 0 :75, andP AB) 0 :25.