If A and B are two events such that $\mathrm{P}\left(\mathrm{A}\right)=\frac{1}{3}, \mathrm{P}\left(\mathrm{B}\right)=\frac{1}{5}$ and $\mathrm{P}(\mathrm{A}\cup \mathrm{B})=\frac{1}{2}$ then P(A|B') + P(B|A') is equal to

$\begin{array}{rcl}P\left(A\right)& =& \frac{1}{3},P\left(B\right)=\frac{1}{5},P\left(A\cup B\right)=\frac{1}{2},\\ P\left(A\cap B\right)& =& \frac{1}{3}+\frac{1}{5}-\frac{1}{2}=\frac{1}{30}\\ P\left(A/B\text{'}\right)+P\left(B/A\text{'}\right)& =& \frac{P\left(A\cap B\text{'}\right)}{P\left(B\text{'}\right)}+\frac{P\left(B\cap A\text{'}\right)}{P\left(A\text{'}\right)}\\ & =& \frac{P\left(A\right)-P\left(A\cap B\right)}{P\left(B\text{'}\right)}+\frac{P\left(B\right)-P\left(A\cap B\right)}{P\left(A\text{'}\right)}\\ & =& \frac{{\displaystyle \frac{1}{3}}-{\displaystyle \frac{1}{30}}}{{\displaystyle \frac{4}{5}}}+\frac{{\displaystyle \frac{1}{5}}-{\displaystyle \frac{1}{30}}}{{\displaystyle \frac{2}{3}}}\\ & =& \frac{3}{8}+\frac{1}{4}=\frac{5}{8}\\ & & \end{array}$