Find the probability that Fred will have a sum of 7, find the probability that Joe and Fred will both have the same sum, and find the probability that billy has a higher sum than 9.

Question

Joe rolls two dice and adds the numbers showing. Fred then rolls two dice and adds the numbers showing.

Answer 1

Which combinations add to 7: 1,6 6,1 2,5 5, 2., 3. 4. 4. 3 that's 6 combinations out of 36 possibilities, so probability is 6/36 = 1/6.

probability both have same sum = probability both have 2 as sum+ probability both have 3 as sum + .... probability both have 12 as sum

to find probability both have 2 as a sum, find probability one has 2 as a sum, then square it.

combinations that have two as a sum: 1, 1 , so probability having 2 as a sum is 1/36

probability both having 2 as a sum is (1/36)^2

combinations that have three as a sum: 1, 2, and 2,1 so probability having 3 as a sum is 2/36. probability both having 3 as a sum is (2/36)^2

and so on until 12.