Question

Suppose you roll 2 dice. What is the probability that the sum of the 2 dice is exactly 8, given that the 1st dice is a 4?

Express your answer as a reduced fraction.

Answer 1

The probability of rolling a sum of 8 with two dice, when the first die shows a 4, is 1/6.

Step-by-step explanation:

When you roll 2 dice and the first die is a 4, the probability that the sum of the two dice is exactly 8 can be calculated by looking at the possible outcomes of the second die.

There is only one outcome that will give us a sum of 8 when the first die is a 4, which is rolling a 4 on the second die (4+4=8).

With a fair six-sided die, the probability of rolling any given number is 1/6.

Therefore, the probability that the sum of the two dice is exactly 8, given that the first die is a 4, is 1/6. This is the only outcome (rolling a 4 on the second die) that will satisfy the condition out of the 6 possible outcomes of rolling the second die.