Numerical answer
Two fair dice are rolled together. The probability that the sum of the numbers shown is a prime number is p/q in lowest terms. Find the value of p+q.
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Answer: 17
Total outcomes = 36. Prime sums possible are 2, 3, 5, 7, 11. Counting favourable outcomes: sum=2 (1 way), sum=3 (2 ways), sum=5 (4 ways), sum=7 (6 ways), sum=11 (2 ways); total = 1+2+4+6+2 = 15. Probability = 15/36 = 5/12 in lowest terms, so p=5, q=12, and p+q = 17.
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