A and B take part in a rifle shooting match. The probability of A hitting the target is 0.4, while the probability of B hitting the target is 0.6. If A has the first shot, post which both strike alternately, then the probability that A hits the targe

Question

A and B take part in a rifle shooting match. The probability of A hitting the target is 0.4, while the probability of B hitting the target is 0.6. If A has the first shot, post which both strike alternately, then the probability that A hits the target before B hits it is

Accepted Answer

P(A wins) = 0.4+0.6⋅0.4⋅0.4+(0.6⋅0.4)2⋅0.4+…=0.4/(1−0.24)=0.4/0.76=10/19.