Quest mutually exclusive events?

**kingyof2thejring** · Oct10-05, 08:59 AM

I've got a question here asking me to explain why events A and B cannot be mutually exclusive events.
P(A)=0.75
P(B)=0.65
And then to comment about P(AuB) and P(AuB)

I've started of by assuming that they are mutually exclusive
and used the addition formula
P(AuB) = P(A) + P(B)
to get an answer greater than 1 therefore cannot be probability function
but I haven't exactly proved that the events A and B are not mutually exclusive events.
Could someone please point me to the right direction.
Thanks in advance

**Hurkyl** · Oct10-05, 09:10 AM

Do you know what a "Proof by contradiction" is?

**HallsofIvy** · Oct10-05, 12:00 PM

If A and B were mutually exclusive, what would P(A and B) be?
What would P(A or B) be?

**kingyof2thejring** · Oct10-05, 04:02 PM

P(A and B) 0.9125
P(A or B) =1.4

Proof by contradiction
State the opposite of what you are trying to prove

Try to draw a conclusion that you know is false or that contradicts something that is true

If that is false, what you are trying to prove must be true. And so you have proved it.

**Hurkyl** · Oct10-05, 04:05 PM

So haven't you done all the steps of a proof by contradiction?

You stated the opposite of what you're trying to prove, and derived something known to be false!