Suppose a pair of dice are rolled. Consider the sum of the numbers on the top of the dice and find the probability.
8, given that at least one die came up 3

Question

Suppose a pair of dice are rolled. Consider the sum of the numbers on the top of the dice and find the probability. ​
8, given that at least one die came up 3
​

Quizplus · Accepted Answer

We can apply conditional probability here. Let A be the event that at least one die came up 3 and B be the event that the sum of the numbers on the top of the dice is 8. Then we want to find P(B|A). We can use the formula:
P(B|A) = P(A and B) / P(A)

To find P(A), we can use the fact that the complement of A (neither die came up 3) is rolling a 2, 4, 5, 6, or 7 on both dice. The probability of this is (20/36)^2 = 25/81. So, P(A) = 1 - 25/81 = 56/81.

To find P(A and B), we can use the fact that one die must have come up 3, so we can list the possible outcomes: (3, 5), (3, 6), (4, 4), (5, 3), (6, 3). There are 5 such outcomes, so P(A and B) = 5/36.

Plugging these values into the formula, we get:
P(B|A) = (5/36) / (56/81) = 5/8
Therefore, the answer is D, 5/8.

Suppose a Pair of Dice Are Rolled