Q256 / 270 · NDA 2017 (Phase 1) · Mathematics

For two dependent events A and B , it is given that $\mathrm{P}(\mathrm{A})=0.2$ and $\mathrm{P}(\mathrm{B})=0.5$. If $\mathrm{A} \subseteq \mathrm{B}$, then the values of conditional probabilites $\mathrm{P}(\mathrm{A} \mid \mathrm{B})$ and $\mathrm{P}(\mathrm{B} \mid \mathrm{A})$ are respectively

  • A
    $\frac{2}{5}, \frac{3}{5}$
  • Correct answer
    B
    $\frac{2}{5}, 1$
  • C
    $1, \frac{2}{5}$
  • D
    Information is insufficient

Solution

$\begin{aligned} & \mathrm{A} \subseteq \mathrm{B} \Rightarrow \mathrm{A} \cap \mathrm{B}=\mathrm{A} \\ & \therefore \mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{B}}\right)=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{B})}=\frac{\mathrm{P}(\mathrm{A})}{\mathrm{P}(\mathrm{B})}=\frac{0.2}{0.5}=\frac{2}{5} \\ & \mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}}\right)=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})}=\frac{\mathrm{P}(\mathrm{A})}{\mathrm{P}(\mathrm{A})}=\frac{0.2}{0.2}=1\end{aligned}$

Hence, the correct answer is option: 'B'.

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