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Question
In a single throw of three dice, find the probability of getting the same number on all the three dice.
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Solution
If three dices are thrown simultaneously, then all the possible outcomes = 63 = 216
∴ Total number of possible outcome, n(S) = 216
Let A be the event of getting the same number on all the three dices.
Then, the favourable outcomes are as follows:
A = {(1, 1, 1), (2, 2, 2), (3, 3, 3), (4, 4, 4), (5, 5, 5), (6, 6 , 6)}
Number of favourable outcomes, n(A) = 6
Hence, required probability, P(A) = P (same number on all the three dices) = \[\frac{6}{216} = \frac{1}{36}\]
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