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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Probability

NDA 2013 · Mathematics · Probability

If P(A)=(2)/(3), P(B)=(2)/(5) , and P(A B)-P(A B)=(2)/(5) , then...

If P(A)=23,P(B)=25\mathrm{P}(\mathrm{A})=\frac{2}{3}, \mathrm{P}(\mathrm{B})=\frac{2}{5}, and P(A∪B)−P(A∩B)=25\mathrm{P}(\mathrm{A} \cup \mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{2}{5}, then what is P(A∩B)\mathrm{P}(\mathrm{A} \cap \mathrm{B}) equal to?

Options

  1. A35\frac{3}{5}
  2. B511\frac{5}{11}
  3. C13\frac{1}{3}
  4. DNone of the above

Correct answer

C. 13\frac{1}{3}

Step-by-step solution

P(A∪B)−P(A∩B)=P(A)+P(B)−2P(A∩B)=25=23+25−2P(A∩B)=25∴P(A∩B)=13\begin{aligned} & \mathrm{P}(\mathrm{A} \cup \mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B}) \\ & =\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-2 \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{2}{5} \\ & =\frac{2}{3}+\frac{2}{5}-2 \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{2}{5} \\ & \therefore \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{3}\end{aligned}
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