AP EAMCET · Maths · Sets and Relations
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
- A \(\frac{1}{5}\)
- B \(\frac{3}{5}\)
- C \(\frac{2}{5}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{5}\)
Step-by-step Solution
Detailed explanation
\(n(A)=\) members proficient in mathematics \(=19\) \(n(B)=\) members proficient in statistics \(=16\) \(\begin{aligned} & n(A \cup B)=n(A)+n(B)-n(A \cap B) \\ & \Rightarrow 25=19+16-n(A \cap B) \\ & \Rightarrow n(A \cap B)=35-25=10\end{aligned}\) Now,…
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