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Q.

unbiased 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

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a

1/3

b

5/21

c

1/4

d

2/5

answer is B.

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Detailed Solution

LetP(S)=P(1 or 2)=1/3P(F)=P(3 or 4 or 5 or 6)=2/3P(A wins )=P[(SS or SFSS or SFSFSS or …)or (FSS or FSFSS or …)]            =191−29+2271−29=19×97+227×97=17+221=3+221=521P(A winning )=521,P(B winning )=1621
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