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Q.

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

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

d

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

answer is D.

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Detailed Solution

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

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

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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