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

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SUMMARY

The calculation of the probability of events A or B, given P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1, is determined using the formula P(A or B) = P(A) + P(B) - P(A and B). This results in P(A or B) = 0.4 + 0.5 - 0.1 = 0.8. The common mistake is to simply add the probabilities of A and B, which incorrectly counts the intersection twice when P(A and B) is greater than zero.

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Homework Statement



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

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The Attempt at a Solution



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

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