Q193 / 270 · NDA 2011 (Phase 1) · Mathematics

If $A$ and $B$ are events such that $\mathrm{P}(A \cup B)=0.5$, $P(\bar{B})=0.8$ and $P(A \mid B)=0.4$, then what is $P(A \cap B)$ equal to?

  • Correct answer
    A
    0.08
  • B
    0.02
  • C
    0.8
  • D
    0.2

Solution

$\begin{array}{rlrl} & \text { Since } & \mathrm{P}(\overline{\mathrm{B}}) & =0.8 \\ \therefore & \mathrm{P}(\mathrm{B}) & =1-\mathrm{P}(\overline{\mathrm{B}}) \\ & =1-0.8=0.2 \\ & & \\ \text { Now } & \mathrm{P}(\mathrm{A} / \mathrm{B}) & =\mathrm{P}(\mathrm{A})=0.4 \\ \text { Now } & \mathrm{P}(\mathrm{A} \cap \mathrm{B}) & =\mathrm{P}(\mathrm{A}) . \mathrm{P}(\mathrm{B}) \\ & & =0.4 \times 0.2=0.08\end{array}$

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

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