Two dice are rolled. Determine the probability of the following. ("Doubles" means both dice show the same number. Enter your probabilities as fractions.)(a)rolling an even sum (b)rolling doubles (c)rolling an even sum and rolling doubles (d)rolling an even sum or rolling doubles

(a) Rolling an even sum: There are 36 possible outcomes when two dice are rolled. An even sum can be obtained in the following 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). That's 18 outcomes. So, the probability is 18/36 = 1/2.

(b) Rolling doubles: Doubles can be obtained in the following ways: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). That's 6 outcomes. So, the probability is 6/36 = 1/6.

(c) Rolling an even sum and rolling doubles: An even sum and doubles can be obtained in the following ways: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). That's 6 outcomes. So, the probability is 6/36 = 1/6.

(d) Rolling an even sum or rolling doubles: This can be obtained in the following ways: all the ways of rolling an even sum (18 outcomes) plus the ways of rolling doubles that are not included in the even sums (0 outcomes, because all doubles give even sums). So, the probability is 18/36 = 1/2.