A and B throw a pair of dice alternately. A wins the game, if he gets a total of 6 anfd B wins, if she gets a total of 7. If a starts the game, then find the probabbility of winning the game by A in third throw of the pair of dice.

Explanation

Let `A_(1)=A` total of 6={(2,4),(1,5),(5,1),(4,2),(3,3)}`
and `B_(1)=A` total of 7={(2,5),(1,6),(6,1),(5,2),(3,4),(4,3)}`
Let P(A) is the probability, If A wins in a throw`rArrP(A)=5/36`
and P(B) is the probability, if B wins in a throw `rArrP(B)=1/6`
`therefore` Required probability=`P(barA)cdotP(barB)cdotP(A)=31/36cdot5/6=(775)/(216cdot36)=775/7776`