A die is tossed twice. Given that the sum is greater than 7, what is the chance of getting a pair?

Question

A die is tossed twice. Given that the sum is greater than 7, what is the chance of getting a pair?

Answer 1

Make a table of possible sums of two die:

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

which combinations give a sum that is greater than 7 (8 or larger), noting the ones that are pairs:

2,6

3,5

3,6

4,4 pair

4,5

4,6

5,3

5,4

5,5 pair

5,6

6,2

6,3

6,4

6,5

6,6 pair

there are 15 combinations that are greater than 7 (8 or larger), 3 of which are pairs.

so given that the combination is greater than 7, the probability is 3/15 = 1/5, that it is a pair