JEE Main 2022 · 28 Jul · Shift 1 · Mathematics Q9

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MathematicsSingle correct+4 / -1Question 9 of 90

Out of 60% female and 40% male candidates appearing in an exam, 60% candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is :

\dfrac34

\dfrac{11}{16}

\dfrac{23}{32}

\dfrac{13}{16}

Answer and worked solution

Official answer: A

Reading the key uses. $P(F)=0.6$ , $P(M)=0.4$ , a female's chance of qualifying is twice a male's ( $2p$ and $p$ ), and $P(Q)=0.6$ .

Solve. $1.2p+0.4p=0.6$ , so $p=\frac38$ , and $P(F\mid Q)=\frac{0.6\times\frac34}{0.6}=\frac34$ .

(Read as head-counts, 40 of the 60 qualifiers would be female, giving $\frac23$ , which is not offered.)

(A)

Topics:Bayes' theorem Conditional probability

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JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 9