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Question
If two different dice are rolled together, the probability of getting an even number on both dice, is:
(A) 1/36
(B) 1/2
(C) 1/6
(D) 1/4
Solution
Possible outcomes on rolling the two dice are given below:
{(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)}
Total number of outcomes = 36
Favourable outcomes are given below:
{(2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6), (6, 2), (6, 4), (6, 6)}
Total number of favourable outcomes = 9
∴ Probability of getting an even number on both dice `="Total numbers of favourable outcomes"/"Total number of outcomes"=9/36=1/4`
Hence, the correct option is D.
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