Problem

Suppose a die is rolled and the possible outcomes are {1, 2, 3, 4, 5, 6}. Let Event A be the event that the outcome is an odd number, and Event B be the event that the outcome is less than 4. Are Events A and B mutually exclusive?

Answer

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Answer

For two events to be mutually exclusive, they cannot have any outcomes in common. However, A and B both include the outcomes 1 and 3, so they are not mutually exclusive.

Steps

Step 1 ：The sample space S of the experiment is S={1,2,3,4,5,6}

Step 2 ：Event A is the event that the outcome is an odd number, so A={1,3,5}

Step 3 ：Event B is the event that the outcome is less than 4, so B={1,2,3}

Step 4 ：For two events to be mutually exclusive, they cannot have any outcomes in common. However, A and B both include the outcomes 1 and 3, so they are not mutually exclusive.

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