Mutually exclusive events
Two events are mutually exclusive if they cannot both happen at once. Their overlap is zero, so P(A or B) is just P(A) + P(B). This is different from being independent.
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Analogy
You cannot be in Paris and Tokyo at the same moment. Those two events exclude each other.
Example
P(heart) = 13/52 = 1/4P(spade) = 13/52 = 1/4P(heart and spade) = 0P(heart or spade) = 1/4 + 1/4 = 1/2
In practice
Drawing one card, being a heart and being a spade are exclusive. The probability of both is 0.
Practice
Flashcards
- Can mutually exclusive events with positive probability be independent?No. If one happens the other cannot, so they affect each other.
Questions people ask
Are mutually exclusive events independent?
No, usually the opposite. If A happens, B cannot, so knowing A changes the chance of B to zero. Independent events do not affect each other at all. Exclusive events with positive probabilities are therefore always dependent, which is why the two ideas should never be confused when you set up a calculation.
How can I tell if two events are mutually exclusive?
Ask whether both can happen in the same trial. Rolling a 2 and rolling an odd number on one die cannot both occur, so they are exclusive. Rolling a 2 and rolling an even number can both occur, so they are not.