Question

Two six-sided dice are rolled (one red and one green). Some possibilities are (Red=1,Green=5) or (Red=2,Green=2) etc.
(a) How many total possibilities are there?

For the rest of the questions, we will assume that the dice are fair and that all of the possibilities in (a) are equally likely.
(b) What is the probability that the sum on the two dice comes out to be 9?

(c) What is the probability that the sum on the two dice comes out to be 12?

(d) What is the probability that the numbers on the two dice are equal?

Answer 1

a.) There are 6^2 = 36 total probabilities.

b.) Sum = 9 are (3, 6), (4, 5), (5, 4), (6, 3)
P(sum = 9) = 4/36 = 1/9

c.) Sum = 12 is (6, 6)
P(sum = 12) = 1/36

d.) Numbers equal are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6)
P(numbers equal) = 6/36 = 1/6