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 ______.

Options

• ${\displaystyle \frac{16}{81}}$

• ${\displaystyle \frac{1}{81}}$

• ${\displaystyle \frac{80}{81}}$

• ${\displaystyle \frac{65}{81}}$

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 ${\displaystyle \frac{16}{81}}$.

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 = ${\displaystyle \frac{4}{6}=\frac{2}{3}}$

∴ q = ${\displaystyle 1-\frac{2}{3}=\frac{1}{3}}$

∴ Required probability = ${\displaystyle {}^4{\text{C}}_4{\left(\frac{2}{3}\right)}^4{\left(\frac{1}{3}\right)}^0=\frac{16}{81}}$