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Probability

Question
CBSEENMA12033730

In a hostel, 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random.
If she reads Hindi newspaper, find the probability that she reads English newspaper.

Solution

Let A and B be two events such that
A : a student reads Hindi newspaper
B : a student reads English newspaper.
therefore space space space space space straight P left parenthesis straight A right parenthesis space equals space 60 over 100 space equals 3 over 5 comma space space space space straight P left parenthesis straight B right parenthesis space equals space 40 over 100 space equals space 2 over 5
space space space space space space space space space space space straight P left parenthesis straight A space intersection space straight B right parenthesis space equals space 20 over 100 space equals 1 fifth
P(she reads English newspaper when it is given that she reads Hindi newspaper) = P(B | A)
equals space fraction numerator straight P left parenthesis straight B intersection straight A right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction space equals fraction numerator straight P left parenthesis straight A space intersection space straight B right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction space equals fraction numerator begin display style 1 fifth end style over denominator begin display style 3 over 5 end style end fraction space equals 1 third

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