# Conditional Probability Question $(X \cup Y)$

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.

• You can deduce this from the pieces of information given. Try drawing a Venn diagram with some overlap of $X$ and $Y$; you should be able to figure out the formula for $P(X|X\cup Y)$ given $P(X)$, $P(Y)$, and one other term, then rearrange it to find the value of the other term, and go from there. – jbowman Sep 30 '18 at 21:55