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How do the ideas independent and mutually exclusive relate to each other?
AThey do not mean the same thing at all
BThey mean the same thing in every case
CMutually exclusive events are always independent
DIndependent events are always mutually exclusive
Answer & Solution
Correct answer: A. They do not mean the same thing at all
1. Mutually exclusive events cannot happen together, so their joint probability is zero.
2. Independent events can happen together, and their joint probability is the product of the two probabilities.
3. The two ideas are therefore different, and a pair of events may satisfy one without satisfying the other.
_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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