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Roll one fair die. C is an odd face larger than two and E is a face less than five. Are C and E mutually exclusive?
AYes, since the two events share no face
BNo, since P(C and E) equals 1/6, not zero
CNo, since P(C and E) equals 2/6, not zero
DYes, since P(C and E) is exactly zero here
Answer & Solution
Correct answer: B. No, since P(C and E) equals 1/6, not zero
1. Event C, the odd faces above two, holds 3 and 5.
2. Event E, the faces below five, holds 1, 2, 3 and 4.
3. The face 3 belongs to both events, so the intersection is not empty.
4. One shared face out of six gives a joint probability of 1/6.
5. Since 1/6 is not zero, C and E are not mutually exclusive.
6. A joint probability of 2/6 would need two shared faces, but 5 lies outside E.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.2 Independent and Mutually Exclusive Events_
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