Single correct option
Two fair dice are rolled. What is the probability that the sum of the numbers shown is a prime number?
- A. 1/3
- B. 7/18
- C. 5/12
- D. 1/2
Show answer and solution
Answer: (C) 5/12
The possible prime sums are 2, 3, 5, 7 and 11.
Number of outcomes for each:
- Sum 2: 1 (1+1)
- Sum 3: 2
- Sum 5: 4
- Sum 7: 6
- Sum 11: 2
Favourable outcomes = 1 + 2 + 4 + 6 + 2 = 15 out of 36.
Probability = 15/36 = 5/12.
Tip: For a sum s from 2 to 7, there are s − 1 ways; for s from 8 to 12, there are 13 − s ways.
Number of outcomes for each:
- Sum 2: 1 (1+1)
- Sum 3: 2
- Sum 5: 4
- Sum 7: 6
- Sum 11: 2
Favourable outcomes = 1 + 2 + 4 + 6 + 2 = 15 out of 36.
Probability = 15/36 = 5/12.
Tip: For a sum s from 2 to 7, there are s − 1 ways; for s from 8 to 12, there are 13 − s ways.
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