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Probability question

2022 · 28 Jul · Shift 1 · Q30
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  5. /2022 · 28 Jul · Shift 1 · Q30

Probability question

2022 · 28 Jul · Shift 1 · Q30

JEE MainMathematicsProbabilityMCQ+4 / −1
Out of 60%60 \%60% female and 40%40 \%40% male candidates appearing in an exam, 60%60 \%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 :
  1. A
    23\frac{2}{3}32​
  2. B
    1116\frac{11}{16}1611​
  3. C
    2332\frac{23}{32}3223​
  4. D
    1316\frac{13}{16}1613​
View written solutionFree

Correct answer: A

  1. Let the total number of candidates be 100100100.

  2. Then:

    • Female candidates =60%= 60\%=60% of 100=60100 = 60100=60
    • Male candidates =40%= 40\%=40% of 100=40100 = 40100=40

  3. Also, 60%60\%60% of all candidates qualify. So total qualified candidates =60%= 60\%=60% of 100=60100 = 60100=60.

  4. Let the number of qualified males be xxx. Then the number of qualified females is twice this, i.e. 2x2x2x.

  5. Since total qualified candidates are 606060, x+2x=60x + 2x = 60x+2x=60 3x=603x = 603x=60 x=20x = 20x=20

    Hence:

    • Qualified males =20= 20=20
    • Qualified females =40= 40=40

  6. Now a candidate is chosen randomly from the qualified candidates. Therefore, the probability that the chosen candidate is a female is number of qualified femalestotal qualified candidates=4060=23.\frac{\text{number of qualified females}}{\text{total qualified candidates}} = \frac{40}{60} = \frac{2}{3}.total qualified candidatesnumber of qualified females​=6040​=32​.

  7. Checking options:

    • A: 23\frac{2}{3}32​ ✅
    • B: 1116\frac{11}{16}1611​
    • C: 2332\frac{23}{32}3223​
    • D: 1316\frac{13}{16}1613​

Therefore, the correct answer is A.

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