Question

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

Answer 1

Let A₁ be the event of getting a total of 6

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

And B₁ be the event of getting a total of 7

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

Let P(A₁) is the probability, if A wins in a throw = `5/36`

And P(B₁) is the probability, if B wins in a throw = `1/6`

∴ The required probability of winning A in his third throw

= `"P"(bar"A"_1) * "P"(bar"B"_1) * "P"("A"_1)`

= `31/36 * 5/6 * 5/36`

= `775/7776`.