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If two dice are thrown, then what is the probability that the sum of the faces of dice are prime?

If two dice are thrown, then what is the probability that the sum of the faces of dice are prime? Correct Answer 5 / 12

The sum may be 2, 3, 5, 7, 11

⇒ 2 can be obtained in 1 way = (1, 1)

⇒ 3 can be obtained in 2 ways = (1, 2), (2, 1)

⇒ 5 can be obtained in 4 ways = (1, 4), (2, 3), (3, 2), (4, 1)

⇒ 7 can be obtained in 6 ways = (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)

⇒ 11can be obtained in 2ways = (5, 6), (6, 5)

∴ Total favorable ways = 1 + 2 + 4 + 6 + 2 = 15

Total outcomes = 62 = 36

P (E) = 15 / 36 = 5 / 12

∴ the required probability is 5 / 12

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