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Question

Aman and Bhuvan throw a pair of dice alternately. In order to win, they have to get a sum of 8. Find their respective probabilities of winning if Aman starts the game.

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Solution

Solution :-
Given A and B throw a dice simultaneously
till one thus gets a 6 and wins the game.
Now, consider winning of A
Let X be obtaining a six by A
Y be obtaining a six by B
A can win the following way :
(i) He obtains a six in the first- trial
(ii) A fails to obtain a six, B fails and A obtain
and so on.
P (A wins) = P(X)+P(XXX)+P(YYYYX)+....
=16+16×(56)2+16×(56)4...
=16×[11(56)2]
=1/612536=611

1112281_1201833_ans_338c386aced640f4b2be17d409d086f2.jpg

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