(A) The total number of outcomes when a die is rolled $4$ times is $6^4 = 1296$.For each roll,the face value must be in the set $\{2, 3, 4, 5\}$ to sa

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(A) The total number of outcomes when a die is rolled $4$ times is $6^4 = 1296$.For each roll,the face value must be in the set $\{2, 3, 4, 5\}$ to satisfy the condition that the minimum is $\ge 2$ and the maximum is $\le 5$.There are $4$ such favorable outcomes for each roll.The number of favorable outcomes for $4$ rolls is $4^4 = 256$.The required probability is $\frac{4^4}{6^4} = \left(\frac{4}{6}\right)^4 = \left(\frac{2}{3}\right)^4 = \frac{16}{81}$.

Class 11 Mathematics Probability Set Based probability

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An unbiased dice 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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A
$16$
B
$1$
C
$80$
D
$65$

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An unbiased dice 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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