So, two mutually exclusive events A and B

P(A or B)=P(A)+P(B).

But what if the probabilities add up to be greater than 1? We can't subtract P(AandB).

Can P(A or B) with mutually exclusive events be greater than 1?

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- Jul 24th 2010, 09:22 AMsfspitfire23mutually exclusive events
So, two mutually exclusive events A and B

P(A or B)=P(A)+P(B).

But what if the probabilities add up to be greater than 1? We can't subtract P(AandB).

Can P(A or B) with mutually exclusive events be greater than 1? - Jul 24th 2010, 09:29 AMPlato
- Jul 24th 2010, 12:16 PMsfspitfire23
So, if P(A)=.9 and P(B)=.9 and the events are mutually exclusive, what is P(A or B)?

- Jul 24th 2010, 12:30 PMPlato
The point is the bit above is impossible. It cannot happen.

Consider, $\displaystyle P(A \cup B) = P(A) + P(B) - P(A \cap B) \leqslant 1$.

From the given $\displaystyle P(A \cap B) \geqslant 0.8$.

**Because $\displaystyle P(A \cap B) \ne 0$ the events are not mutually exclusive.**