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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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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)) "P(M )" = Probability that person selected is male Since it is assumed that there are equal number of males & females, "P(M)" = 1/2 = 0.5 "P(G|M) "= Probability of selected a grey haired male = 5% = 5/100 = 0.05 "P(F)" = Probability that person selected is female "P(F)" = 1/2 = 0.5 "P(G|F) "= Probability of selected a grey haired female = 0.25% = 0.25/100 = 0.0025 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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.