In question 64 (above), $P\left( {B/{A^\prime }} \right)$ is equal to

$P\left( {B/{A^\prime }} \right) = \frac{{P\left( {B \cap {A^\prime }} \right)}}{{P\left( {{A^\prime }} \right)}} = \frac{{P(B) - P(B \cap A)}}{{1 - P(A)}}$

$= \frac{{\frac{3}{5} - \frac{3}{{10}}}}{{1 - \frac{1}{2}}} = \frac{{\frac{{6 - 3}}{{10}}}}{{\frac{1}{2}}} = \frac{6}{{10}} = \frac{3}{5}$