Single correct option
Two fair dice are thrown. Given that at least one of them shows an even number, what is the probability that the sum of the numbers shown is a prime number?
- A. 5/12
- B. 14/27
- C. 7/18
- D. 15/36
Show answer and solution
Answer: (B) 14/27
Outcomes with at least one even number = 36 − (both odd) = 36 − 9 = 27.
Prime sums: 2, 3, 5, 7, 11. A sum of 2 is (1,1) — both odd, excluded. Any odd sum needs one odd and one even die, so all such outcomes are in the conditioning set.
Count: sum 3 → 2, sum 5 → 4, sum 7 → 6, sum 11 → 2 → total 14.
Required probability = 14/27.
Trap: 15/36 is the unconditional probability of a prime sum.
Prime sums: 2, 3, 5, 7, 11. A sum of 2 is (1,1) — both odd, excluded. Any odd sum needs one odd and one even die, so all such outcomes are in the conditioning set.
Count: sum 3 → 2, sum 5 → 4, sum 7 → 6, sum 11 → 2 → total 14.
Required probability = 14/27.
Trap: 15/36 is the unconditional probability of a prime sum.
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