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Probability
NCERT Class 12
CBSE
Grade 12

Question:

Suppose 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.

Step-by-Step Solution

$P(E_1) = 1/2, P(E_2) = 1/2$. [1.0 Mark]
$P(G|E_1) = 0.05, P(G|E_2) = 0.0025$. [1.5 Marks]
Bayes' formula: $\dfrac{0.05}{0.05 + 0.0025} = \dfrac{0.05}{0.0525}$. [1.5 Marks]
$P(E_1|G) = \dfrac{20}{21}$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Evaluating prior gender probabilities: 1.0 Mark
Evaluating conditional grey hair probabilities: 1.5 Marks
Formulating Bayes' fraction: 1.5 Marks
Evaluating final probability $= 20/21$: 1.0 Mark

Correct Answer:
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