Problem Solving

swerve wrote:Two fair die with sides numbered 1 to 6 are tossed. What is the probability that the sum of the exposed faces on the die is a prime number?

A. \(\frac{5}{11}\)

B. \(\frac{5}{12}\)

C. \(\frac{5}{21}\)

D. \(\frac{2}{9}\)

E. \(\frac{5}{36}\)

The OA is B

Source: Manhattan Prep

The prime numbers between 2 and 12, inclusive, are 2, 3, 5, 7, and 11. The possible pairings with a sum being a prime number are:

(1,1), (2,1), (1,2), (1,4), (4,1), (3,2), (2,3), (4,3), (3,4), (6,1), (1,6), (2,5), (5,2), (6,5), (5,6)

Recall that there are 36 possible outcomes from rolling two 6-sided dice. Thus, the probability that the sum is a prime number is 15/36 = 5/12.

Answer: B