Mutually exclusive events are events that cannot happen at the same time. Think of it like flipping a coin: you can only get heads or tails, not both simultaneously!
Independent events are events where the outcome of one does not affect the outcome of the other. Rolling a die and then flipping a coin are independent events because the result of the die roll doesn't change the probability of getting heads or tails.
| Feature | Mutually Exclusive Events | Independent Events |
|---|---|---|
| Definition | Events that cannot occur at the same time. | Events where the outcome of one does not influence the outcome of the other. |
| Occurrence | If one event occurs, the other cannot. | The occurrence of one event does not change the probability of the other. |
| Probability | $P(A \cap B) = 0$ | $P(A \cap B) = P(A) * P(B)$ |
| Example | Flipping a coin: getting heads and tails on the same flip. | Rolling a die and flipping a coin. |
| Overlap | No overlap in outcomes. | Outcomes can overlap. |
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