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How many of the three independence conditions must you verify to prove that two events are independent?
AAll three of the conditions must be shown
BExactly two of the conditions must be shown
CNone, since independence cannot be proved
DOnly one of the conditions must be shown
Answer & Solution
Correct answer: D. Only one of the conditions must be shown
1. Three equivalent conditions define independence, covering the two conditionals and the product rule.
2. Because they are equivalent, any one of them implies the other two.
3. Showing only one of them is therefore enough, and which one you pick depends on the information you have.
4. Failing that single test makes the events dependent rather than independent.
_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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