A and B throw a dice alternatively till one of them gets a number greater than four and wins the - Maths - Probability

Question

A and B throw a dice
alternatively till one of them gets a number greater than
four and wins the game If A starts the game, what
is the probability of B winning?

Anuradha Sharma · Accepted Answer

Probability of winning = getting a number greater than 4or getting 5 and 6 = 26=13So probability of loosing = 1-13=23Now if we want that B wins so AloseBwin+AloseBloseAloseBwin+AloseBloseAloseBloseAloseBwin+
=23×13+23×23×23×13+23×23×23×23×23×13
It is a GP with first term a = 29 and common ratio r = 49So sum of infinite GP series=a1-r=291- 49=25

A and B throw a dice alternatively till one of them gets a number greater than four and wins the game. If A starts the game, what is the probability of B winning?