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 :

Mathematics · Probability

JEE Main 2024 — 9 April, Shift 2 — Question 17

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text {th }}$ roll than the number obtained

in the $(\mathrm{i}-1)^{\text {th }}$ roll, $\mathrm{i}=2,3$ , is equal to :

Favourable cases $={ }^{6} \mathrm{C}_{3}$

Total out comes $=6^{3}$

Probability of getting greater number than previous one $=\frac{{ }^{6} \mathrm{C}_{3}}{\mathrm{r}^{3}}=\frac{20}{216}=\frac{5}{54}$

Answer key and solution verified before publishing.

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