1. ## Probability

Theres one thing in stats i dont fully understand and thats the cases when you're asked to find the probability of something given that something has already happened. For example on my homework i'm given this question:

A and B are two events: P(A)=0.32, P(B)=0.5 and P(AÈB)=0.55

Find P(notA|B)

I would of thought that it would of been solvable by P(notAÇB) / P(B)

Which would extend to P(notA) + P(B) - P(notAÈB)/P(B)

But its the P(notAÈB) and P(notAÇB) that throws me, because im not 100% on how to solve them without having the other one.

Any help would be appreciated

2. $A^c$ means not A.
Then $P(A^c |B) = 1 - P(A|B)$ & $P(A \cap B) = P(A) + P(B) - P(A \cup B)$.

3. It is helpful to picture P(not A n B) in the Venn Diagram.
It is simply the region B outside of A, which is found by taking 0.55-0.32 = 0.23.

As we know P(not A|B) is a ratio, it's P(not AnB) / P(B) = 0.46