Bunuel
There are two lines of defense against an attacking aircraft, the first is a missile and the second an anti-aircraft gun. The respective probabilities that the aircraft being hit by the missile and the gun are 2/9 and 1/8, respectively. What is the probability of hitting the aircraft ?
A. 23/72
B. 1/3
C. 25/72
D. 13/36
E. 3/8
Solution:
We use the complement rule to solve this problem. There are 4 possible outcomes in this scenario, where H = the aircraft is hit and N = the aircraft is not hit:
(H, H) means the aircraft is hit by both the missile and the gun
(H, N) means the aircraft is hit by the missile but not the gun
(N, H) means the aircraft is not hit by the missile but is hit by the gun
(N, N) means the aircraft is hit by neither the missile nor the gun
Note that any of the first 3 outcomes would indicate a hit. So only the fourth outcome (N, N) is the outcome where the aircraft is not hit. Thus, it is easier to calculate the probability of (N, N) and subtract this probability from 1 (using the rule of the complement) to find the probability that the aircraft is hit.
The probability of not hitting the aircraft by either the missile or the gun - (N, N) - is (1 - 2/9) x (1 - 1/8) = 7/9 x 7/8 = 49/72. Thus, the probability of hitting the aircraft is 1 - 49/72 = 23/72.
Answer: A