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

Step-by-step solution

P ( P )= 3 4 , P ( Q )= 1 2 , P ( R )= 5 8 Since P , Q , R are independent events, P ^ , Q ^ , R ^ are also independent events. aligned & P( Target is hit by P or Q but not R) = & P (P Q ^ R ^ )+P ( P ^ Q R ^ ) & P ( P Q R ^ ) = & P ( P ) P ( Q ^ ) P ( R ^ )+ P ( P ^ ) P ( Q ) P ( R ^ ) & + P ( P ) P ( Q ) P ( R ^ ) = & ( 3 4 ) ( 1 2 ) ( 3 8 )+ ( 1 4 ) ( 1 2 ) ( 3 8 )+ ( 3 4 ) ( 1 2 ) ( 3 8 ) = & 9+3+9 64 = & 21 64 aligned