Q. A dice is rolled three times. The probability of getting a larger number than the previous number each time is
A) $\frac{15}{216}$
B) $\frac{5}{54}$
C) $\frac{13}{216}$
D) $\frac{1}{18}$
Explanation
(b)
The total number of ways $= 6^{3} = 216$
If the second number is $i(i > 1)$, then the total number of favourable ways
$= \sum_{i = 1}^{5}{(i - 1)(6 - i) = 20}$
$\therefore\$ Required probability $= \frac{20}{216} = \frac{5}{54}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.