Misc 3 - Suppose 5% of men and 0.25% of women have grey hair - Miscellaneous

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  1. Chapter 13 Class 12 Probability
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Misc 3 Suppose that 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. Let M : Male F : Female G : Grey hair Person We need to find the Probability that the person selected is male, if the person is grey haired i.e. P(M|G) P(M|G) = 𝑃 𝑀﷯.𝑃(𝐺|𝑀)﷮𝑃 𝐹﷯. 𝑃 𝐺|𝐹﷯ + 𝑃 𝑀﷯. 𝑃(𝐺|𝑀)﷯ Putting value in formula, P(M|G) = 0. 5 ×0 . 05﷮0. 5 × 0. 0025 + 0. 5 × 0. 05﷯ = 0. 5 × 0 . 05﷮ 0. 5 0. 0025 + 0. 05﷯ ﷯ = 0.05﷮0.0525﷯ = 500﷮525﷯ = 𝟐𝟎﷮𝟐𝟏﷯ Therefore, required probability is 20﷮21﷯

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