CUET · MATHS · PYQ PAPER 2023
Suppose \(10 \backslash \%\) of men and \(0.5 \backslash \%\) of women have grey hair. A grey haired person is selected at random. If there are equal number of males and females, then the probability of the selected person being a female is :
- A \(\frac{20}{21}\)
- B \(\frac{1}{21}\)
- C \(\frac{1}{200}\)
- D \(\frac{1}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{21}\)
Step-by-step Solution
Detailed explanation
\(P(M) = 0.5, P(F) = 0.5\) \(P(G|M) = 0.10, P(G|F) = 0.005\) \(P(G) = P(G|M)P(M) + P(G|F)P(F) = (0.10)(0.5) + (0.005)(0.5) = 0.05 + 0.0025 = 0.0525\) \(P(F|G) = \frac{P(G|F)P(F)}{P(G)} = \frac{(0.005)(0.5)}{0.0525} = \frac{0.0025}{0.0525}\)…
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