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Plain English Definition:
Two events are mutually exclusive if they cannot happen at the same time. If one happens, the other definitely didn't happen.
Real-world examples:
The Good News:
If events can't overlap, there's no double-counting problem! We can just add the probabilities directly.
Remember the general formula:
When A and B are mutually exclusive, P(A ∩ B) = 0, so the formula simplifies to:
What is the probability of rolling a number that is less than 3 OR greater than 4?
Outcomes: 1, 2 →
Outcomes: 5, 6 →
No! Think about it: a number would need to be smaller than 3 (like 1 or 2) but also bigger than 4 (like 5 or 6). That's impossible!
The overlap is empty:
Since these events are mutually exclusive, just add:
Final Answer:
Which numbers satisfy "less than 3 OR greater than 4"?
Notice: 3 and 4 are in the "dead zone" — they satisfy neither condition.
When events are mutually exclusive (no overlap possible), the union formula simplifies:
No need to subtract anything — there's nothing to double-count!