Conditional probability mixing Union and Intersect - $P(A\cap B\mid A\cup B)$

Question

Could someone help with how the formula is applied to these sort of problems with conditional probability?

I have $P(A) = 0.5$, $P(B) = 0.3$, $P (A\cap B) = 0.1$ I was able to calculate $P(A\cup B)$ from set theory as $= 0.5+0.3-0.1 = 0.7$

But where do I go from here? Thank you!

Answer 1

HINT

Since $A\cap B \subseteq A\cup B$, we can proceed as follows

\begin{align*} \mathbb{P}(A\cap B|A\cup B) & = \frac{\mathbb{P}((A\cap B)\cap(A\cup B))}{\mathbb{P}(A\cup B)} = \frac{\mathbb{P}(A\cap B)}{\mathbb{P}(A\cup B)} \end{align*}

Can you take it from here?