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With A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8} and C = {7, 9}, which pair is mutually exclusive?
AA and B, which share two outcomes
BB and C, which share one outcome
CA and C, which share no outcome
DNo pair here is mutually exclusive
Answer & Solution
Correct answer: C. A and C, which share no outcome
1. A and B both hold 4 and 5, so their joint probability is 2/10 and they are not mutually exclusive.
2. B and C both hold 7, so their joint probability is not zero either.
3. A and C have no number in common, so their joint probability is zero.
4. A and C are therefore the mutually exclusive pair.
_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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