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A die is rolled, and the number that falls uppermost is observed. Let E denote the event that the number shown is even, and let F denote the event that the number is odd number.
A. Are the events E and F mutually excluseve?
B. Are the evnts # and F complementary?

• Math -

Out of the possible numbers (in the sample space), if you cannot represent both events (odd and even) by a single outcome, then the events are mutually exclusive. In this case, we cannot have a number which is both odd and even, so E and F are mutually exclusive.

Events A and B are complementary if they are
1. mutually exclusive, AND
2. A∪B make up the sample space.

In the case of E and F, the sample space is
Ω={1,2,3,4,5,6},
E={2,4,6}
F={1,3,5}
so
E∪F={1,2,3,4,5,6}=Ω
Therefore E and F are complementary.

• Math -

Thank you

• Math -

You're welcome!

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