Question

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

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

Answer 1

The correct option is A $\frac{16}{81}$

When we roll a die for 4 time total cases are: $6\times 6\times 6\times 6$

Favored cases are when we got numbers:$2,3,4,5$ $=4$ numbers

Probability for this case$=\frac{4\times 4\times 4\times 4}{6\times 6\times 6\times 6}=\frac{16}{81}$