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 b

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:

TestHub · Accepted Answer

Let probability of hitting target by P is E 1 , Q is E 2 ,and by R is E 3 From the question Required probability is P ( E 1 ) P ( E 2 ) P ( E 3 ¯ ) + P ( E 1 ¯ ) P ( E 2 ) P ( E 3 ¯ ) + P ( E 1 ) P ( E 2 ¯ ) P ( E 3 ¯ ) = 3 4 1 2 3 8 + 1 4 1 2 3 8 + 3 4 1 2 3 8 = 12 + 9 64 = 21 64

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