Two dice are rolled. Determine the probability of the following. (Enter your probabilities as fractions.)(a)rolling an even sum(b)rolling a sum greater than 7(c)rolling an even sum and a sum greater than 7(d)rolling an even sum or a sum greater than 7

(a) Rolling an even sum:

There are 36 possible outcomes when two dice are rolled. An even sum can be obtained in 18 ways (1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6). So, the probability of rolling an even sum is 18/36 = 1/2.

(b) Rolling a sum greater than 7:

A sum greater than 7 can be obtained in 15 ways (2,6), (3,5), (3,6), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,2), (6,3), (6,4), (6,5), (6,6). So, the probability of rolling a sum greater than 7 is 15/36 = 5/12.

(c) Rolling an even sum and a sum greater than 7:

An even sum greater than 7 can be obtained in 6 ways (2,6), (4,4), (4,6), (6,2), (6,4), (6,6). So, the probability of rolling an even sum and a sum greater than 7 is 6/36 = 1/6.

(d) Rolling an even sum or a sum greater than 7:

The events of rolling an even sum and rolling a sum greater than 7 are not mutually exclusive, so we add the probabilities of the two events and subtract the probability of the intersection (which we calculated in part (c)). So, the probability of rolling an even sum or a sum greater than 7 is (1/2) + (5/12) - (1/6) = 4/6 + 5/12 - 2/12 = 8/12 + 5/12 - 2/12 = 11/12.