Q75 / 160 · AP EAMCET 2023 (16 May Shift 1) · Mathematics

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
    $\frac{3}{5}$
  • Correct answer
    C
    $\frac{2}{5}$
  • D
    $\frac{1}{2}$

Solution

$n(A)=$ 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, $P(A \cap B)=\frac{n(A \cap B)}{25}=\frac{10}{25}=\frac{2}{5}$

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

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