An unbiased die with faces marked 1, 2, 3, 4, | vedclass

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(A) Let $X_1, X_2, X_3, X_4$ be the outcomes of the four rolls.We want the probability that $2 \le X_i \le 5$ for all $i = 1, 2, 3, 4$.For each roll,t

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$16$

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(A) Let $X_1, X_2, X_3, X_4$ be the outcomes of the four rolls.We want the probability that $2 \le X_i \le 5$ for all $i = 1, 2, 3, 4$.For each roll,the possible outcomes are $\{1, 2, 3, 4, 5, 6\}$,so there are $6$ total outcomes.The favorable outcomes for each roll are $\{2, 3, 4, 5\}$,which gives $4$ favorable outcomes.The probability of a single roll resulting in a value between $2$ and $5$ inclusive is $p = \frac{4}{6} = \frac{2}{3}$.Since the four rolls are independent,the probability that all four rolls result in values between $2$ and $5$ is $p^4 = (\frac{2}{3})^4 = \frac{16}{81}$.

An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of the four face values obtained,the probability that the minimum face value is not less than $2$ and the maximum face value is not greater than $5$ is: (in $/81$)

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