P: Independence and mutually exclusive events are different
Independence means learning one event occurred does not change the probability of the other. Mutual exclusivity means they cannot occur together. Nonzero mutually exclusive events cannot be independent. Test the definition with the joint probability, not with how unrelated the event names sound.
Worked example or practice scenario
If P(A)=.3 and P(B)=.4, independent events have P(A∩B)=.12 and P(A∪B)=.58. Mutually exclusive events with the same marginal probabilities instead have joint probability zero and union probability .7.
Try this next
For each interpretation, compute P(A|B). It is .3 in the independent case and zero in the mutually exclusive case. Add a third example where events overlap but are dependent.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.
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