JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Probability

Out of

60%

female and

40%

male candidates appearing in an exam,

60%

candidates qualify it. The number of females qualifying the exam is three times 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 :

(A) $\frac{3}{4}$ ✓ Correct
(B) $\frac{11}{16}$
(C) $\frac{23}{32}$
(D) $\frac{13}{16}$

Answer: (A)

Solution

Take

100

candidates:

60

are female and

40

are male, and

60

qualify in all. When the qualifying females are three times the qualifying males,

15

males and

45

females qualify. Choosing one of the

60

qualified candidates, the chance that the one chosen is female is

\frac{45}{60} = \frac{3}{4}

JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Single correct option

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