Question
Two fair dice are thrown. What is the probability that
the sum is a prime number?Solution
ATQ, Possible sums that are prime: 2, 3, 5, 7, 11 Count ways: Sum 2: (1,1) -> 1 way Sum 3: (1,2),(2,1) -> 2 ways Sum 5: (1,4),(2,3),(3,2),(4,1) -> 4 ways Sum 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) -> 6 ways Sum 11: (5,6),(6,5) -> 2 ways Total favourable = 1 + 2 + 4 + 6 + 2 = 15 Total outcomes = 6*6 = 36 Probability = 15/36 = 5/12
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