A fair coin is tossed repeatedly until two consecutive heads is obtained. If the probability that two
consecutive heads occur on the seventh and eight flips is equal to $\frac{a}{b}$ (where a, b are co primes and a,b $\in$ N) then $[\frac{b}{2 a}] =________$ (where [.] is denoted by greatest integer function)

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answer is A.

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Detailed Solution

First five (no consecutive heads) 5T or 4T,1H or 3T, 2H or 2T, 3H
i.e:TTTTTTHH or HTTTTTHH or HTHTTTHH OR HTHTHTHH
Required probability $= \frac{1 + 5_{C_{1}} + 4 c_{2} + 3_{C_{3}}}{2^{8}} = \frac{13}{256}$

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