I cannot seem to solve this conditional probability question.
Suppose $X$ and $Y$ are two events from a sample space with $\Pr(X) = 0.25$, $\Pr(Y) = 0.5$ and $\Pr(X|X \cup Y) = 0.5.$ Find $\Pr(X \cup Y)$.
I know that the union of $X$ and $Y$ will be:
$$ \Pr(X \cup Y) = \Pr(X) + \Pr(Y) - \Pr(X ∩ Y) $$
But I am having issues finding $(X ∩ Y)$. I think this is linked to Bayes Theorem in some way but I am going in circles.