Two persons A and B take part in a shooting competition. A can hit the target with a probability of 0.6 . B can hit the target with a probability of 0.8 . A has the first shoot, past which they strike alternatively. Then, the probability that A wins the competition is

Step-by-step solution

Given that, P(A)=0.6 and P(B)=0.8 P (A^ )=0.4 and (P (B^ )=0.2 . Probability that A wins =P(A)+P (A^ ) P (B^ ) P(A)+P (A^ ) P (B^ ) P (A^ ) P (B^ ) P(A)+ aligned P(A wins )=0.6+(0.4)(0.2)(0.6)+( & (0.4)^2 & (0.2)^2(0.6)+ . aligned P(A wins )= 0.6 1-(0.4 0.2) [ above series is an infinite GP series with a=0.6 and r=0.4 0.2 ] P(A wins )= 0.6 1-0.08 = 60 92 P(A wins )= 15 23