Question

2 dice are rolled 8 times, what is the probability distribution for a sum of seven?

I know it's 1/6, but how would I go about drawing a probability histogram for this question?

Answer 1

The sample space has 36 possible combinations of numbers. These can be set out in column form as follows:
6,6 5,6 4,6 3,6 2,6 1,6
6,5 5,5 4,5 3,5 2,5 1,5
6,4 5,4 4,4 3,4 2,4 1,4
6,3 5,3 4,3 3,3 2,3 1,3
6,2 5,2 4,2 3,2 2,2 1,2
6,1 5,1 4,1 3,1 2,1 1,1

As you can see, the probability of rolling a sum of 7 is 6/36 = 1/6.
Each time the dice are rolled the probability of rolling a sum of 7 is 1/6.
The required distribution fits the criteria for a binomial distribution, therefore we need to calculate the probabilities of 1, 2, 3, 4, 5, 6 and 7 sums of 7 when the pair is rolled 7 times.