Two dice are rolled. Find the probability that the sum was a 7 given that one of the numbers was a
5.
A)1/6
B)1/12
C)2/11
D)1/11

Question

Quizplus · Accepted Answer

We can use conditional probability to solve this problem. Let A be the event that the sum is 7 and B be the event that one of the numbers is 5. We want to find P(A | B), the probability that the sum is 7 given that one of the numbers is 5.

There are 6 possible outcomes when rolling two dice and getting a 5 on one of them: (5,1), (5,2), (5,3), (5,4), (5,6), and (1,5), (2,5), (3,5), (4,5), (6,5). Out of these, only (2,5), (3,4), and (4,3) have a sum of 7. Therefore, P(A and B) = 3/36 = 1/12, and P(B) = 11/36 (there are 11 outcomes that have at least one 5).

Using the formula for conditional probability, we have P(A | B) = P(A and B)/P(B) = (1/12)/(11/36) = 2/11. Therefore, the answer is choice C. There are 6 possible outcomes when one of the dice is a 5: (5,1), (5,2), (5,3), (5,4), (5,6), and (1,5), (2,5), (3,5), (4,5), (6,5). Among these, only (2,5), (3,4), and (4,3) have a sum of 7. Therefore, the probability that the sum is 7 given that one of the numbers was a 5 is 3/6 or 2/11.

Two Dice Are Rolled