How to determine Probability of a 4 and 6 sided die.

Question

A fair four-sided die and a fair six-sided die are rolled. Write down the sample space of all possible outcomes. (Fairness means all these simple outcomes have the same probability of occurrence.) Let A denote the sum of the numbers on the top faces is ≥ 14. Let B be the event that the sum of the numbers on the top faces is ≤ 16. Are the events A and B mutually exclusive?

I have the first part There are 24 possible outcomes.

S= (1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (3,4) (4,1) (4,2) (4,3) (4,4) (5,1) (5,2) (5,3) (5,4) (6,1) (6,2) (6,3) (6,4)

but the second part of this question is really getting to me, I don't believe i am thinking of it the right way. If i denote A to be the sum of the numbers on the top faces is ≥ 14 then its 0, because the highest roll you can do with those two dice are a 4 and a 6. I know I must be thinking this the wrong way. Any help will be greatly appreciated.

Answer 1

This is checking that you understand mutually exclusive, which means the two events cannot both happen. If one cannot happen, then both cannot, so they are mutually exclusive.

Answer 2

Presuming you've copied the question down correctly here, I don't think you're thinking of anything wrong; the question appears to be trivial (i.e. have an uninteresting answer). One of two things appears to be the case:

Option 1: Either you've mis-copied a problem, or there's a misprint in the problem text, or something like that. (Best guess -- did you mean product instead of sum to define these events?)

Option 2: Maybe the instructor / text / whatever intended for you to think through a trivial event. As written, you're right; the probability of event $A$ is $0$.