Two events are known to be mutually exclusive. What does that tell you about whether they are independent?
AThey are independent
BThey are dependent
CThey are impossible
DNothing on its own
Answer & Solution
Correct answer: D. Nothing on its own
1. Mutually exclusive and independent are two separate tests on a pair of events.
2. The test for mutually exclusive is whether the probability of both together is zero.
3. The test for independent is whether the probability of both together equals the product of the two separate probabilities.
4. Passing one test says nothing on its own about the other, so both must be checked.
5. Events can be mutually exclusive and independent, or one and not the other, in different combinations.
_Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 10: Probability_
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