Final answer:
The probability that the total of two dice will be greater than 7 when the first die shows a 5 is 2/3, as the second die must roll a 3, 4, 5, or 6.
Step-by-step explanation:
To find the probability that the total of two dice will be greater than 7 given that the first die shows a 5, we need to consider the possible outcomes of the second die. Since the first die is a 5, the second die must show a number greater than 2 to achieve a total greater than 7 (i.e., 3, 4, 5, or 6).
There are 4 favorable outcomes (3, 4, 5, 6) out of 6 possible outcomes for the second die, so the probability of rolling a number greater than 2 on the second die is 4/6 or 2/3.
Therefore, the probability that the total will be greater than 7, when the first die shows a 5, is 2/3.