Question

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.
Find the probability that she reads neither Hindi nor 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(student reads neither Hindi nor English newspaper)
$equals space straight P left parenthesis straight A to the power of straight c space and space straight B to the power of straight c right parenthesis space equals space straight P space open square brackets open parentheses straight A space union space straight B close parentheses to the power of straight c close square brackets space equals space 1 space space minus space straight P left parenthesis straight A space union space straight B right parenthesis space equals space 1 minus open square brackets straight P left parenthesis straight A right parenthesis space plus space straight P left parenthesis straight B right parenthesis space minus space straight P left parenthesis straight A space intersection space straight B right parenthesis close square brackets space equals space 1 minus open square brackets 3 over 5 plus 2 over 5 minus 1 fifth close square brackets space equals space 1 minus 4 over 5 space equals space 1 fifth$

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Probability

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.
Find the probability that she reads neither Hindi nor English newspaper.

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For Daily Free Study Material Join wiredfaculty

Probability

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.Find the probability that she reads neither Hindi nor English newspaper.

Some More Questions From Probability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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.
Find the probability that she reads neither Hindi nor English newspaper.