Question

Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are 3/4, 1/2  and 5/8, respectively, then the probability that the target is hit by P or Q but not by R is

(A) 39/64

(B) 21/64

(C) 15/64 

(D) 9/64

Answer 1

Answer is (B) 21/64

We have the following probabilities: 

• The probability that the target is hit by the person P is 3/4. 

• The probability that the target is not hit by the person P is 1 - 3/4 = 1/4. 

• The probability that the target is hit by the person Q is 1/2.

• The probability that the target is not hit by the person Q is 1 - 1/2 = 1/2.

• The probability that the target is hit by the person R is 5/8.

• The probability that the target is not hit by the person R is 1 - 5/8 = 3/8. 

Here, we have used the fact that if the probability of occurrence of an event is p, then the probability of non-occurrence of an event is q = 1 – p. 

Therefore, the probability that the target is hit by P or Q and not by R is (Probability that the target is hit by P and not by Q and R + (Probability that the target is hit by Q and not by P) and R + Probability that the target is hit by both P and) (Q and not by R)