# A red die and a green die are thrown, and the numbers of each are noted. Which pairs of the following events are mutually exclusive?

i have a final exam tomorrow and i have this question in one of the old exams that i couldn't understand how to solve it.

A red die and a green die are thrown, and the numbers of each are noted. Which pairs of the following events are mutually exclusive? E={both are even}, F={both are odd}, G={sum is 2}, H={sum is 4}, I={sum is greater than 10}.

can you explain it for me ?

• Welcome to Math.SE, faisal! What have you tried? At least a couple of these should be intuitive. Do you know what it means for the pairs of events to be mutually exclusive? Dec 27, 2013 at 16:03

Hint: Note that if two events are mutually exclusive it means that if one is true then the other must not be true. For instance, in your case you have that $E$ and $F$ are mutually exclusive because if both die are even, then they cannot be both odd, for a number cannot be simultaneously odd and even.
The best way would be to write up all patterns if you don't understand it well. $$E=\{(2,2), (2,4),\cdots\}$$ $$F=\{(1,1),(1,3),\cdots\}$$ $$G=\{(1,1)\}$$ Then, comparing these will give you the answer. Do your best!