If an unbiased dice is rolled thrice, then the probability o... | Mathematics | SolveeIt | Solveeit

Today, August 23

Question

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i$ -th roll than the number obtained in the $(i-1)$ -th roll, $i = 2, 3$ , is equal to:

A

$\frac{3}{54}$

B

$\frac{2}{54}$

C

$\frac{5}{54}$

D

$\frac{1}{54}$

Answer

$\frac{5}{54}$

Explanation

Solution

Favorable Cases: $\binom{6}{3}$

Total Outcomes: $6^3$

Probability of selecting numbers such that each is greater than the previous:

$P = \frac{\binom{6}{3}}{6^3} = \frac{20}{216} = \frac{5}{54}$