# Probability with Intersections, Unions, and Complements

I just want to make sure I'm doing this correctly.

Here is the problem:

Let $A$ and $B$ be sets such that $P(A \cap B)=\frac{1}{4}, P(\tilde{A})=\frac{1}{3},$ and $P(B)=\frac{1}{2}$. What is $P(A \cup B)$?

My answer is $\frac{11}{12}$ and here is my reasoning:

$P(\tilde{A})=\frac{1}{3}$, therefore, $P(A)=\frac{2}{3}$.

$P(A \cup B)=P(A)+P(B)-P(A \cap B)=\frac{2}{3} + \frac{1}{2} - \frac{1}{4}=\frac{11}{12}$

Question:
Does this make sense or I am just making stuff up?

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That's perfectly correct. –  Robert Israel Sep 14 '11 at 22:47