Four persons can hit a target correctly with probabilities 1 2 , 1 3 , 1 4 and 1 5 respectively. If all hit at the target independently, then the probability that the target would be hit, is

Step-by-step solution

Let event A : A can hit the target event B : B can hit the target event C : C can hit the target event D : D can hit the target P ( ~A )= 1 2 , P ( ~B )= 1 3 , P ( C )= 1 4 , P ( D )= 1 5 P (Target is not hit by any one of them) = P ( ~A ^ B ^ C ^ D ^ )= P ( A ^ ) P ( B ^ ) P ^ ( C ^ ) P ( D ^ )= ( 1 2 ) ( 2 3 ) ( 3 4 ) ( 4 5 )= 1 5 aligned & P ( Target is hit ) & =1- P ( Target is not hit by any one of them ) & =1- 1 5 & = 4 5 aligned