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Question
Two different dice are rolled simultaneously. Find the probability that the sum of numbers appearing on the two dice is 10 ?
Solution
The first die could show any one of the numbers 1, 2, 3, 4, 5, 6. The same is true for the second die as well.
The possible outcomes are:
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
The outcomes favourable to event, E are {(4, 6), (5, 5), (6, 4)}.
∴ Number of outcomes favourable to event, E = 3
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