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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 ?

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  • $\begingroup$ 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? $\endgroup$ Dec 27, 2013 at 16:03

3 Answers 3

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In this question, mutually exclusive refers to the pairs of sets that have no elements in common.

Put another way, you want to list the pairs of sets where their intersection is the empty set.

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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.

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  • $\begingroup$ Thanks a lot. so, the answer is: (E & F, E & G, F & I) are mutually exclusive is that right ? $\endgroup$
    – faisal
    Dec 27, 2013 at 16:38
  • $\begingroup$ @faisal Yes, they appear to be the correct mutually exclusive combinations. $\endgroup$ Dec 27, 2013 at 16:39
  • $\begingroup$ @faisal G&H, G&I, and H&I, are also mutually exclusive! $\endgroup$ Feb 24, 2014 at 4:58
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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!

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