Question

An unbiased dice 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 

(A) 16/81 

(B) 1/81 

(C) 80/81 

(D) 65/81

Answer 1

Answer is (A) 16/81

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

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

Hence,

required probability = ⁴C₄(2/3)⁴(1/3)⁰ = 16/81