Question

A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, the find the probability that B wins.

Answer 1

Let A be the event that A gets a total of 7 and B be the event of B getting total of 10

A : gets a total of 7,

   A = {1,6), (6,1), (2,5), (5,2), (3,4), (4,3)}

B : gets a total of 10,

      B = {(4,6) (6,4), (5, 5)}

In a single throw,

Hence, we get an infinite G.P with first term as 5/72 and common ratio as 55/72.