P , Q and R try to hit the same target one after the other. If their probabilities of hitting the target are 2 3 , 3 5 , 5 7 respectively, then the probability that the target is hit by P or Q but not by R is

Step-by-step solution

Let P= The event that P hit target Q = The event that Q hit target R = The event that R hit target P ( P )= 2 3 , P ( Q )= 3 5 and P ( R )= 5 7 Now, required probability aligned & = P ( P ) P ( Q ^ ) P ( R ^ )+ P ( P ^ ) P ( Q ) P ( R ^ )+ P ( P ) P ( Q ) P ( R ^ ) & = 2 3 2 5 2 7 + 1 3 3 5 2 7 + 2 3 3 5 2 7 = 8+6+12 105 = 26 105 aligned