Question

An unbiased die with face marked 1, 2, 3, 4, 5, 6 is rolled four times. Out of 4 face values obtained, find the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5.

Answer 1

$$\begin{gathered} P\left(\text{face value is not more than 5 and not less than 2}\right)=\frac{4}{6}=\frac{2}{3} \\ P\left(\text{face value is not more than 5 and not less than 2 in 4 throws}\right)=\frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3} \\ =\frac{16}{81} \end{gathered}$$