How do you calculate the probability of A or B when there is an intersection?

[g.lemaitre]

Homework Statement

If P(A) = .4, P(B) = .5 and P(A and B) = .1, find P(A or B)

Homework Equations

The Attempt at a Solution

Why isn't the answer just .9, add the two probabilities together? The book says the answer is .8

 

[g.lemaitre]

I got it now. I didn't see this equation

P(A or B) = P(A) + P(B) - P(A and B)

.4 + .5 - .1 = .8

 

[voko]

That would work, if A and B were disjoint. But you have P(A and B) > 0, so there is some intersection. If you just take P(A or B) = P(A) + P(B), you count that intersection TWICE.