Question

$$\begin{gathered} P\left(\frac{X}{Y}\right) =\frac{P(X\cap Y)}{P\left(Y\right)}= \frac{1}{2} \\ P\left(\frac{Y}{X}\right) =\frac{P(X\cap Y)}{P\left(X\right)}= \frac{2}{5} \\ \Rightarrow P(X\cap Y) =\frac{2}{15} \\ P\left(Y\right)=\frac{4}{15} also P(X\cup Y) =\frac{7}{15} \\ P\left(\frac{X\text{'}}{Y}\right) = 1-P\left(\frac{X}{Y}\right) =1-\frac{1}{2}=\frac{1}{2} \end{gathered}$$