Consider three coins having probabilities of obtaining head in a single trail as $\frac{1}{4}, \frac{1}{2} and \frac{3}{4}$ , respectively. A player selects one of these three coins at random (each coin is equally likely to be selected). If the player tosses the selected coin five times independently, then the probability of obtaining two tails in five tosses is equal to

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$\frac{64}{384}$

$\frac{125}{384}$

$\frac{85}{384}$

$\frac{255}{384}$

answer is A.

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Detailed Solution

$= \frac{1}{3} \times^{5} C_{2} [{(\frac{1}{4})}^{3} {(\frac{3}{4})}^{2} + {(\frac{1}{2})}^{2} + {(\frac{3}{4})}^{7} {(\frac{1}{4})}^{2}] = \frac{10}{3} (\frac{9 + 32 + 27}{256 \times 4}) = \frac{85}{384}$

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