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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Probability

NDA 2011 · Mathematics · Probability

If A and B are events such that P(A B)=0.5 , P( B )=0.8 and P(A...

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

Options

  1. A0.08
  2. B0.02
  3. C0.8
  4. D0.2

Correct answer

A. 0.08

Step-by-step solution

 Since P(B‾)=0.8∴P(B)=1−P(B‾)=1−0.8=0.2 Now P(A/B)=P(A)=0.4 Now P(A∩B)=P(A).P(B)=0.4×0.2=0.08\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}
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