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Question

# A fair die is tossed repeatedly. A wins if it is 1 or 2 on two consecutive tosses and B wins if it is 3,4,5 or 6 on two consecutive tosses. The probability that A wins if the die is tossed indefinitely is

A
13
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B
521
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C
14
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D
25
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Solution

## The correct option is C 521Say, A won the first round, Then for A to win, the possible combinations are :AA,ABAA,ABABAA, and so on.The probability of A winning is : 13(13+29.13+...) where 29 is the probability of the group AB.P(Awins given that A wins the first round)=13.13.97 where 97=(1+29+...)P(A wins given that A wins the first round)=17 ...(1)If B won the first round , then similarly for A to win we have,BAA,BABAA,BABABAA,...Hence the total probability is 23.19.97 =221P(A wins given that B wins the first round)=221 ...(2)Adding the probabilities (1) and (2), we get 17+221=521

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