two persons A and B play a game of throwing a pair of dice until one of them wins.A will win if sum of numbers on dice appear to be 6and B will win,if sum is 7.What is the probability that A wins the game if A starts the game

Dear Student ,

There are total of 36 outcomes when you throw a pair of dice .Let P(A) be the probability of winning of A , so automatically P(A') will be the probability of losing of A .

Same for B let P(B) be the probability of its winning then automatically P(B') will be the probability of its losing .

Now P(A) = 5 / 36 and P(A') = 31 /36 ;

Similarly P(B) = 6/36 and P(B') = 30 / 36 . Now

Let P be the probability that A wins if A starts the game first . Then P will be given by :

P = P(A) + P(A')*P(B) + P(A')*P(B')*P(A) + ............... .

P = 5 /36 + 31/36 * 6/36 + 31/36 * 30/36 * 5/36 ............

Now usually the series that came here , it will act as a G.P. but here it is not any type of series . Might some information is missing out in the question . Check it again and let me know  .

Hope you understand the basic concept of it . Feel free to ask , the comment box is open 24*7 .