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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

P(minimum face value not less than 2 and maximum face value is not greater than 5)
$=P\left(2or3or4or5\right)=\frac{4}{6}=\frac{2}{3}$
Hence required probability ${=}^4{C}_4{\left(\frac{2}{3}\right)}^4{\left(\frac{1}{3}\right)}^0=\frac{16}{81}$