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 die is showing a 5?
If one die is 5, there is an equal probability that the second die will be 1 through 6, and that the total will be 6,7,8,9,10 or 11. So the answer is 1/6
To find the probability that the sum of the upturned faces on a pair of dice is 8, given that one die is already showing a 5, we need to consider the possible outcomes and the favorable outcomes.
Step 1: Determine the total number of outcomes when two dice are rolled.
When two dice are rolled, each die can have 6 outcomes (numbers 1 to 6). Therefore, the total number of outcomes is 6 * 6 = 36.
Step 2: Identify the favorable outcomes.
Since one die is already showing a 5, the second die needs to show 3 to result in a sum of 8 (5 + 3 = 8). So, the favorable outcome is when the second die shows a 3.
Step 3: Calculate the probability.
The probability can be calculated by dividing the number of favorable outcomes by the total number of outcomes.
Number of favorable outcomes = 1 (when the second die shows 3)
Total number of outcomes = 36
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 1 / 36
Hence, the probability that the sum showing is 8, given that one die is showing a 5, is 1/36.