If an unbiased dice is rolled thrice, then the probability of getting a greater number in the roll than the number obtained in the roll, is equal to

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Solution

Q.
If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{t h}$ roll than the number obtained in the ${(i - 1)}^{t h}$ roll, $i = 2, 3,$ is equal to [2024]

1 $\frac{5}{54}$

2 $\frac{2}{54}$

3 $\frac{1}{54}$

4 $\frac{3}{54}$

Ans.
(1)

Let X be the event of getting a greater number than the previous one in a throw of a die.

Favourable outcomes to $X = {}^{6}{C_{3}}$

[ $∵$ ${}^{6}{C_{3}}$ are ways of getting 3 outcomes one less than other as we have total 6 possible outcomes]

Total outcomes = $6^{3}$

$P (X) = \frac{{}^{6}{C_{3}}}{6^{3}} = \frac{20}{216} = \frac{5}{54}$

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