Question 252145
When you roll two (2) dice, the total number of possibilities is the product of the number of sides of the first die, M, and the second die, N, or MN. In this case our total is 24.

(a) P(A) = the probability of getting the sum of 5. We can list these ways very easily in first die - second die form as: 1-4, 2-3, 3-2, 4-1. Yes you are allowed to reverse the numbers due to the different die. We see P(A) = 4/24 = 1/6.

(b) P(B) = the probability of getting the sum of 5 or 9. We can list these also very easily. We already know the sum of 5 is in 4 ways. THe sum of 9 is created in only 2 ways: 6-3, 5-4. Now, the word "OR" means add, so, P(B) = 4/24 + 2/24 = 6/24 = 1/4.

(c) P(A n B) = P(A) + P(B) - P(A u B). This is a good formula to remember. You can get it using Venn diagrams. We actually, have everything we need. It is easier not to reduce in this question until the end.
P(A n B) = 4/24 + 6/24 - (4/24 + 6/24) = 0.

It will be zero, because you can't get both the sum of a 5 AND the sum of a 9.