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An unbiased cubical die is thrown $5$ times. The probability that the maximum number appearing on the die is $4$ is

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$7 / 6^{5}$

$781 / 6^{5}$

$3781 / 6^{5}$

$1781 / 6^{5}$

answer is B.

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Detailed Solution

Let $X =$ maximum number appearing on the cubical die.

$\begin{matrix} P (X = 4) = P (X \leq 4) - P (X \leq 3) \\ = {(\frac{4}{6})}^{5} - {(\frac{3}{6})}^{5} = {(\frac{2}{3})}^{5} - {(\frac{1}{2})}^{5} = \frac{2^{5}}{3^{5}} - \frac{1}{2^{5}} = \frac{781}{6^{5}} \end{matrix}$

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