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In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to

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a

\frac{200}{6^{5}}

b

\frac{150}{6^{5}}

c

\frac{225}{6^{5}}

d

\frac{175}{6^{5}}

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detailed solution

Correct option is D

$\begin{matrix} 1 \\ 4 \\ 4 \\ 4 \end{matrix} \begin{matrix} 2 \\ 4 \\ 4 \\ 4 \end{matrix} \begin{matrix} 3 \\ 4 \\ 4 \\ 4 \end{matrix} \begin{matrix} 4 \\ 4 \\ 4 \\ 4 \end{matrix} \begin{matrix} 5 \\ 4 \\ 4 \\ 4 \end{matrix} \begin{matrix} no of ways \\ {(\frac{5}{6})}^{3} {(\frac{1}{6})}^{2} \\ {(\frac{5}{6})}^{2} {(\frac{1}{6})}^{3} \\ {(\frac{5}{6})}^{2} {(\frac{1}{6})}^{3} \end{matrix}$

Total $= \frac{125 + 25 + 25}{6^{5}} = \frac{175}{6^{5}}$

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