Question

An unbaised 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 then

• A. $16/81$
• B. $1/81$
• C. $80/81$
• D. $65/81$

Answer 1

The correct option is A $16/81$

Let $p=$ probability of getting face value not less than $2$ and not more than $5$ in a single throw of die $=4/6=2/3$
$n=$ number of times die is rolled
$X=$ number of times we get a number not less than $2$ and not more than $5$.
Then by bernoulli distribution $XB(n,p)$
Required probability $=P(X=4){=}^4{C}_4{p}^4=(2/3{)}^4=16/81$.