A and B plays a game. They alternately roll a fair die and the first person to roll a 6 wins the game. If A starts, what is the probability of A wining the game?

prob of winning =1/6

prob of losing =5/6

now let A win in 1st go then prob=1/6

if A lose in 1st go then A will win in 3rd go so B has to lose in his 1st go so

(5/6)*(5/6)*(1/6)

when A win in 3rd go then

(5/6)^4*1/6

this will go tiill infinity

1/6+(5/6)^2*1/6+(5/6)^4*1/6..............

sum of infinite terms of GP

a/1-r

1/6*(1/(1-25/36)

6/9=2/3