Event A: Rolling an odd number on a fair die. Event B: Rolling a 4 on a fair die. Event C: Rolling an even number on a fair die. Given the three events, which of the following statements is true? Select all that apply.

Event A: Rolling an odd number on a fair die.

Event B: Rolling a 4 on a fair die.

Event C: Rolling an even number on a fair die.

Given the three events, which of the following statements is true? Select all that apply.

Not quite right - check out the answer explanation.

Event A and Event B are mutually exclusive.

Event B and Event C are mutually exclusive.

Event A and Event C are not mutually exclusive.

Event A and Event C are mutually exclusive.

Answer Explanation
Correct answer:
Event A and Event B are mutually exclusive.

Event A and Event C are mutually exclusive.

Remember that in general, A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B)=0.

In this question, note that A={1,3,5} and B={4} have no outcomes in common. Therefore, A and B are mutually exclusive.

Similarly, C={2,4,6}, which has no outcomes in common with A. Therefore, A  and C are mutually exclusive.

 

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