# mutually exclusive events

• Jul 24th 2010, 10:22 AM
sfspitfire23
mutually 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, 10:29 AM
Plato
Quote:

Originally Posted by sfspitfire23
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?

The answer is no. Not in the same probability space
• Jul 24th 2010, 01:16 PM
sfspitfire23
So, if P(A)=.9 and P(B)=.9 and the events are mutually exclusive, what is P(A or B)?
• Jul 24th 2010, 01:30 PM
Plato
Quote:

Originally Posted by sfspitfire23
So, if P(A)=.9 and P(B)=.9 and the events are mutually exclusive, what is P(A or B)?

The point is the bit above is impossible. It cannot happen.
Consider, $P(A \cup B) = P(A) + P(B) - P(A \cap B) \leqslant 1$.
From the given $P(A \cap B) \geqslant 0.8$.
Because $P(A \cap B) \ne 0$ the events are not mutually exclusive.