Question

Franklin rolls a pair of six-sided fair dice with sides numbered 1 through 6.
The probability that the sum of the numbers rolled is either even or a multiple of 5 is . The probability that the sum of the numbers rolled is either a multiple of 3 or 4 is .

Answer 1

it's asking for two probabilities:
1. "the sum is either even or a multiple of 5"
2. "the sum is either a multiple of 3 or 4"

the principle for both is the same. consider all the possibilities (1,2,3,4,5,6 on each dice, added together), count the # of possibilities that apply to the conditions, and divide by the total # of outcomes (36, for rolling two dice. otherwise, 6*6)

Answer 2

for 1:
there are 18 even sums (count them yourself to confirm) and 6 multiples of 5. however you cannot stop here, because you have to consider that the 10's are double-counted (they are both even and multiples of 5). so simply subtract how many 10's appear.

I'll let you do the second part, using the same process.