Question

Cathy rolled a pair of fair dice. What is the probability of getting a prime number as a sum of the numbers appearing on the dice?

• A. $\frac{7}{12}$
• B. $\frac{5}{18}$
• C. $\frac{5}{12}$
• D. $\frac{12}{5}$

Answer 1

The correct option is C $\frac{5}{12}$

Total sample space when two dice are rolled is:

We can get a minimum of 2 (2 = 1 + 1) or a maximum of 12 (12 = 6 + 6) as the sum.

Total prime numbers that can be obtained are:
2, 3, 5, 7, 11

For 2, the outcomes must be (1, 1).
So, we have 1 favorable outcome.

For 3, the outcomes must be (1, 2) or (2, 1).
So, we have 2 favorable outcomes.

For 5, the outcomes must be (1, 4), (4, 1), (2, 3), or (3, 2).
So, we have 4 favorable outcomes.

For 7, the outcomes must be (1, 6), (6, 1), (2, 5), (5, 2), (3, 4) or (4, 3).
So, we have 6 favorable outcomes.

For 11, the outcomes must be (5, 6) or (6, 5).
So, we have 2 favorable outcomes.

Total favorable outcomes are:
1 + 2 + 4 + 6 + 2 = 15

Total outcomes are 36.

$\text{Probability}=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}$

$\text{Probability}=\frac{15}{36}$

$\text{Probability}=\frac{5}{12}$