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प्रश्न
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.
उत्तर
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`.
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