## Question

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face times. Out of 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 then,

### Solution

16/81

Let *p* = probability of getting face a value not jess than 2 and not more than 5 in a single throw of die = 4/6 = 2/3.

n = number of times die is rolled

X = number of times we get a number not less than 2 and not more than 5.

Then *X* ~ *B* (*n*, *p*)

Required probability

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