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If an unbiased dice is rolled thrice, then the probability of getting a greater number in the ith roll than the number obtained in the (i - 1)th roll, i = 2, 3, is equal to
(1) 5/54
We need x1 < x2 < x3. Any 3 different numbers out of 6 can be arranged in increasing order in exactly one way, so favourable cases = 6C3 = 20.
Total cases = 63 = 216
Probability = 20216 = 554
Answer: (1)
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