$\text{ Let }A\text{ and }B\text{ be two events such that }P\left(A\cap B^{\mathrm{\prime }}\right)=0.20\text{, }P\left(A^{\mathrm{\prime }}\cap B\right)=0.15,P\left(A^{\mathrm{\prime }}\cap B^{\mathrm{\prime }}\right)=0.1\text{, then }P(A/B)\text{ is equal to}$

$P\left(A\cap B^{\mathrm{\prime }}\right)=P\left(A\right)-P(A\cap B)=0.20$

and

$\begin{array}{r}\mathrm{P}\left({\mathrm{A}}^{\mathrm{\prime }}\cap \mathrm{B}\right)=\mathrm{P}\left(\mathrm{B}\right)-\mathrm{P}(\mathrm{A}\cap \mathrm{B})=0.15\\ \Rightarrow \mathrm{P}\left(\mathrm{A}\right)+\mathrm{P}\left(\mathrm{B}\right)-2\mathrm{P}(\mathrm{A}-\mathrm{B})=0.35\end{array}$

now

$\begin{array}{l}\mathrm{P}\left({\mathrm{A}}^{\mathrm{\prime }}\cap {\mathrm{B}}^{\mathrm{\prime }}\right)=1-\mathrm{P}(\mathrm{A}\cup \mathrm{B})\\ \Rightarrow 0.1=1-\mathrm{P}\left(\mathrm{A}\right)-\mathrm{P}\left(\mathrm{B}\right)+\mathrm{P}(\mathrm{A}\cap \mathrm{B})\\ \Rightarrow \mathrm{P}\left(\mathrm{A}\right)+\mathrm{P}\left(\mathrm{B}\right)-\mathrm{P}(\mathrm{A}\cap \mathrm{B})=0.9\\ \Rightarrow \mathrm{P}(\mathrm{A}\cap \mathrm{B})=0.9-0.35=0.55\end{array}$

and

$\mathrm{P}\left(\mathrm{A}\right)=0.75,\mathrm{P}\left(\mathrm{B}\right)=0.70$

now

$\mathrm{P}(\mathrm{A}/\mathrm{B})=\frac{\mathrm{P}(\mathrm{A}\cap \mathrm{B})}{\mathrm{P}\left(\mathrm{B}\right)}=\frac{0.55}{0.70}$