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.

(a) Find the probability that she reads neither Hindi nor English newspapers.

(b) If she reads Hindi newspaper, find the probability that she reads English newspaper.

(c) If she reads English newspaper, find the probability that she reads Hindi newspaper

Given:

Let H and E denote the number of students who read Hindi and English newspaper respectively.

Hence, P(H) = Probability of students who read Hindi newspaper=

P(E) = Probability of students who read English newspaper =

P (H ∩ E) = Probability of students who read Hindi and English both newspaper =

(a) Find the probability that she reads neither Hindi nor English newspapers.

P(neither H nor E)

P(neither H nor E) = P(H^{’} ∩ E^{’})

As, { H^{’} ∩ E^{’} =(H ∪ E)^{’}}

⇒ P(neither A nor B) = P ((H ∪ E)^{’})

= 1 - P (H ∪ E)

= 1- [P(H) + P(E) - P (H ∩ E)]

(b) If she reads Hindi newspaper, find the probability that she reads English newspaper.

P (E|H) = hindi newspaper reading has already occurred and the probability that she reads English newspaper is to find.

As we know

⇒

⇒ P (E|H) =

(c) If she reads English newspaper, find the probability that she reads Hindi newspaper.

P (H|E) = English newspaper reading has already occurred and the probability that she reads Hindi newspaper is to find.

As we know

⇒

⇒ P (H|E) =

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