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Question
Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is a prime number?
Solution
According to the question,
Two dice are thrown simultaneously.
So, that number of possible outcomes = 36
Sum of the numbers appearing on the dice is a prime number i.e., 2, 3, 5, 7 and 11.
So, the possible outcomes are (1, 1), (1, 2), (2, 1), (1, 4), (2, 3), (3, 2), (4, 1), (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1), (5, 6) = (6, 5).
Hence, number of possible outcomes = 15
∴ The probability that the sum of the numbers appearing on the dice is a prime number = `15/36 = 5/12`
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