Two persons A and B are throwing an unbiased six faced dice alternatively, with the condition that the person who throws 3 first wins the game. If A starts the game, then probabilities of A and B to win the same are, respectively

Step-by-step solution

Here, probability of success, p= 1 6 and probability of failure. q= 5 6 Let A starts the game, then aligned & A= 1 6 + ( 1 6 ) ( 5 6 )^2+ ( 1 6 ) ( 5 6 )^4+ . . & P(A)= 1 6 1- ( 5 6 )^2 = 1 6 1- 25 36 & = 1 6 11 36 = 6 11 aligned Total probability, P(A)+P(B)=1 aligned & P(B)=1-P(A) & =1- 6 11 = 5 11 aligned