Please Help!!!

A pair of dice are rolled and the sum on their upturned faces is recorded. WHat is the probability that the sum showing is 8, given that one dice is showing a 5?

When one AND ONLY ONE die shows a five, the other die can show 1 through 6 with equal probability. However, the possibility of a 5 is excluded becasue you have said that only one die had a five. You are asking for the probability of throwing a 3 with the "other" die. That is 1/5, for outcomes with only one five showing.

To find the probability of getting a sum of 8 when one die is showing a 5, let's break down the possible outcomes step by step.

Step 1: Determine the probability of rolling a 5 with one die. Since each die has 6 possible outcomes (numbers 1 to 6), the probability of rolling a 5 is 1/6.

Step 2: Once we know that one die is showing a 5, the only way to obtain a sum of 8 is if the other die shows a 3 (5 + 3 = 8).

Step 3: Again, since each die has 6 possible outcomes, the probability of rolling a 3 is also 1/6.

Step 4: To calculate the probability of both events occurring (one die showing a 5 and the other a 3), we multiply the probabilities together: (1/6) * (1/6) = 1/36.

Therefore, the probability of getting a sum of 8, given that one die is showing a 5, is 1/36.