Q29 of 45 Page 1

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


According to Bayes Theorem, if E1, E2, E3,………. En are a set of mutually exclusive and exhaustive events,


Then


Let E1 be the event that the selected person is male and E2 be the event that its a female.


P(E1)=12=P(E2)


E1 and E2 are mutually exclusive and exhaustive, so we can apply Bayes theorem.


Let E: be the event that the person has grey hair. 5% of men picked at random have grey hair →


It can be calculated also the probability:


=


The required probability is .


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