We roll two fair dice, one red and one blue. Find the probability of each.

Question

(A) P(total is 7 and one is 3)=

(B) P(both are odd and one is greater than 4)=

Answer 1

The fact that one is red and one is blue has no bearing on these questions so we can ignore that.

There are 36 total possible outcomes (dice 1 can have 6 possibilities and dice 2 can have 6 possibilities and 6•6 = 36).

The number of possibilities that are 7 are (1, 6) (2, 5) (3, 4) (4, 3) (5, 2) and (6, 1) and only two of these have 3's in them. So the probability that the total is 7 AND one of the dice is 3 is 2/36 or 1/18

For question b), there are the same number of even outcome as odd outcomes on each dice (1, 3, 5) for odd and (2, 4, 6) for even. Meaning each dice has 3 odd outcomes so there are 3•3 or 9 possible outcomes where both are odd (1,1) (1, 3) (1, 5) (3, 1) (3, 3) (3, 5) (5, 1) (5, 3) and (5, 5). The outcomes where one of the dice is greater than 4 are then (1, 5) (3, 5) (5, 1) (5, 3) and (5, 5) so 5 possible outcomes. That means the probability that both are odd and one is greater than 4 is 5/36