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. $\frac{16}{81}$
• B. $\frac{1}{81}$
• C. $\frac{80}{81}$
• D. $\frac{65}{81}$

Answer 1

Answer: (A)

$\frac{16}{81}$

Let $p=$ Probability of getting face value not less than $2$ and not more than $5$ in a single throw of die $=\frac{4}{6}=\frac{2}{3}$
$n=$ number of times dice is rolled
$x=$ number of times we get a number not less than $2$ and not more than $5$.
Then, $X\sim B(n,p)$
$\therefore$ Required probability $=P(X=4){=}^4{C}_4.p^4={\left(\frac{2}{3}\right)}^4=\frac{16}{81}$