A pair of fair dice is cast. What is the probability that the sum of the numbers falling uppermost is less than 5, if it is known that one of the numbers is a 2?

Question

A pair of fair dice is cast. What is the probability that the sum of the numbers falling uppermost is less than 5, if it is known that one of the numbers is a 2? ​

Quizplus · Accepted Answer

If one of the numbers is a 2, then there are only 6 possible outcomes:
{(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)}

Out of these 6 possible outcomes, only (2,1) and (2,2) have a sum that is less than 5.

Therefore, the probability of getting a sum less than 5, given that one of the numbers is a 2, is 2/6 or 1/3.

Choice A is the only one that matches this probability (1/3).

A Pair of Fair Dice Is Cast