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, $i=2,3$, is equal to :

JEE Main · 2024 · 09 Apr 2024 · Shift 2 · Probability

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 :

Answer: (C)

We need

x_{1} < x_{2} < x_{3}

, the three rolls forming a strictly increasing sequence. Any 3 distinct values chosen from

{1, \dots, 6}

have exactly one arrangement (increasing order) that satisfies this, so the number of favourable outcomes is

(3 6) = 20

Total outcomes

= 6^{3} = 216

P = \frac{20}{216} = \frac{5}{54}

JEE Main · 2024 · 09 Apr 2024 · Shift 2 · Single correct option