Question

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four 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 ______.

पर्याय

• `16/81`

• `1/81`

• `80/81`

• `65/81`

Answer 1

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four 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 `16/81`.

Explanation:

P(minimum face value not less than 2 and maximum face value is not greater than 5)

= P(2 or 3 or 4 or 5) = p = `4/6 = 2/3`

∴ q = `1 - 2/3 = 1/3`

∴ Required probability = `""^4"C"_4 (2/3)^4 (1/3)^0 = 16/81`