Question

What is the probability of rolling a number less than or equal to 8 with the

sum of two dice, given that at least one of the dice must show a 6?

Answer 1

Answer:
9/36=1/4

Step-by-step explanation:
I'm going to solve this in this way - we know that there are
6.6=36 different results we can get from rolling 2 dice, so in this probability fraction, 36 is the denominator.
We're constrained that one die must be a 6 and the total must be equal to or greater than 8.
When die A is 6, die B can be 2-6 but can't be 1, so we have 5 acceptable results.
When die B is 6, die A can be 2-6 but can't be 1, so we have 5 more acceptable results.
Now note that we've just double counted the (6,6) result, so we take away 1 good result, and end up with 9 and a total probability of
9/36=1/4

Answer 2

1/3

Step-by-step explanation:

If one die is a 6, then the possible sums are:

1 + 6 = 7

2 + 6 = 8

3 + 6 = 9

4 + 6 = 10

5 + 6 = 11

6 + 6 = 12

Of the 6 possibilities, 2 are less than or equal to 8.

P = 2/6 = 1/3.