Question

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.

Solution

Let E₁, E₂, E be the events
E₁ : ‘selected person is a male’
E₂ : ‘selected person is a female’,
E : ‘selected person is grey haired’
$therefore$ $straight P left parenthesis straight E subscript 1 right parenthesis space equals space straight P left parenthesis straight E subscript 2 right parenthesis space equals space 1 half.$
and $straight P left parenthesis straight E space vertical line space straight E subscript 1 right parenthesis space equals space 5 over 100 space equals 1 over 20 comma space space space space straight P left parenthesis straight E space vertical line space straight E subscript 2 right parenthesis space equals fraction numerator 0.25 over denominator 100 end fraction equals 1 over 400.$
Required probaility = $straight P left parenthesis straight E subscript 1 space vertical line space straight E right parenthesis$
$fraction numerator equals space straight P left parenthesis straight E subscript 1 right parenthesis thin space straight P left parenthesis straight E space vertical line space straight E subscript 1 right parenthesis over denominator straight P left parenthesis straight E subscript 1 right parenthesis thin space straight P left parenthesis straight E space vertical line space straight E subscript 1 right parenthesis space plus space straight P left parenthesis straight E subscript 2 right parenthesis thin space straight P left parenthesis straight E space vertical line thin space straight E subscript 2 right parenthesis end fraction equals space fraction numerator begin display style 1 half end style cross times begin display style 1 over 20 end style over denominator begin display style 1 half end style cross times begin display style 1 over 20 end style plus begin display style 1 half end style cross times begin display style 1 over 400 end style end fraction space equals fraction numerator begin display style 1 over 20 end style over denominator begin display style 1 over 20 end style plus begin display style 1 over 400 end style end fraction space equals fraction numerator begin display style 1 over 20 end style over denominator begin display style fraction numerator 20 plus 1 over denominator 400 end fraction end style end fraction space equals fraction numerator begin display style 1 over 20 end style over denominator begin display style 21 over 400 end style end fraction equals space 1 half cross times 400 over 21 space equals 20 over 21.$

For Daily Free Study Material Join wiredfaculty

Probability

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.

Some More Questions From Probability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction