Q. 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) $\frac{65}{81}$
Explanation
(a)
Let $A =$ getting not less than 2 and not greater than 5.
$\Rightarrow A = \{ 2,\ 3,\ 4,\ 5\}$
$\Rightarrow P(A) = \frac{4}{6}$
But dice is rolled four times, therefore the probability in getting four throws.
$= \left( \frac{4}{6} \right)\left( \frac{4}{6} \right)\left( \frac{4}{6} \right)\left( \frac{4}{6} \right) = \frac{16}{81}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.