Mathematics - Probability Question with Solution | TestHub

$\begin{array}{rl}& \mathrm{P}(\mathrm{A})=\frac{7}{10},\mathrm{P}(\mathrm{B})=\frac{4}{10}\\ & \mathrm{P}(\mathrm{A}\cup \overline{\mathrm{B}})=\frac{5}{10}\\ & \mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}\cup \overline{\mathrm{B}}}\right)=\frac{\mathrm{P}(\mathrm{B}\cap (\mathrm{A}\cup \overline{\mathrm{B}}))}{\mathrm{P}(\mathrm{A}\cup \overline{\mathrm{B}})}\\ & =\frac{\mathrm{P}((\mathrm{B}\cap \overline{\mathrm{B}})\cup (\mathrm{B}\cap \mathrm{A}))}{\mathrm{P}(\mathrm{A}\cup \overline{\mathrm{B}})}=\frac{\mathrm{P}(\mathrm{A}\cap \mathrm{B})}{\mathrm{P}(\mathrm{A}\cup \overline{\mathrm{B}})}\end{array}$
$\begin{array}{rl}& =\frac{\mathrm{P}(\mathrm{A})-\mathrm{P}(\mathrm{A}\cap \overline{\mathrm{B}})}{\mathrm{P}(\mathrm{A})+\mathrm{P}(\overline{\mathrm{B}})-\mathrm{P}(\mathrm{A}\cap \overline{\mathrm{B}})}=\frac{\frac{7}{10}-\frac{5}{10}}{\frac{7}{10}+\left(1-\frac{4}{10}\right)-\frac{5}{10}}\\ & =\frac{2}{8}=\frac{1}{4}\end{array}$