How do I find the following probabilities?
P(A|A ∪ B)
P(A|A ∩ B)
P(A ∩ B|A ∪ B)
P(A|A ∪ B)
P(A|A ∩ B)
P(A ∩ B|A ∪ B)
?
P(A/AB) = P(A (AB)) / P(AB)
P(A/AB) = P(A(AB)) / P(AB)
P(AB/AB) = P(AB) (AB) / P(AB).
Dixon
P(Q I S) means reduce your world down to just S. What fraction of it is Q?
And it is Q/S
P(A|A ∪ B) = A/(A ∪ B)
P(A|A ∩ B)
Even in words the probability of A given the intersection of A and B is clearly 1.
P(A ∩ B|A ∪ B) = (A ∩ B)/(A ∪ B)