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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Sets and Relations

JEE Main · Mathematics · Sets and Relations

In a committee of 25 members, each member is proficient either in...

In a committee of 25 members, each member is proficient either in Mathematics or in Statistics or in both. If 19 of them are proficient in Mathematics and 16 of them are proficient in Statistics, then the probability that a person selected at random from the committee is proficient in both is

Options

  1. A15\frac{1}{5}
  2. B35\frac{3}{5}
  3. C25\frac{2}{5}
  4. D12\frac{1}{2}

Correct answer

C. 25\frac{2}{5}

Step-by-step solution

n(A)=n(A)= members proficient in mathematics =19n(B)==19n(B)= members proficient in statistics =16=16n(A∪B)=n(A)+n(B)−n(A∩B)⇒25=19+16−n(A∩B)⇒n(A∩B)=35−25=10\begin{aligned} & n(A \cup B)=n(A)+n(B)-n(A \cap B) \\ & \Rightarrow 25=19+16-n(A \cap B) \\ & \Rightarrow n(A \cap B)=35-25=10\end{aligned}$Now,Now,P(A \cap B)=\frac{n(A \cap B)}{25}=\frac{10}{25}=\frac{2}{5}$
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