Question

Al and Bill each have two bullets. They fire alternately at a glass bottle. Al has hitting probability 1/3 and Bill 1/4. What is the probability that Al smashes the bottle if he is the one who fires the first shot? (Note: Al can smash the bottle even if he misses with his first shot.)

Answer 1

P(Al hits bottle first time) = 1/3
P(Al misses the first shot but hits on his second shot) =  
P( Al misses and bill misses and Al hits) = 2/3 * 3/4 * 1/3 = 1/6

So required probability = 1/3 + 1/6 =  1/2