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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 read neither Hindi nor English newspaper.
(b) If she reads Hindi newspaper, find the probability that she reads English newspaper also.
(c) If she reads English newspaper, find the probability that she reads Hindi newspaper also.

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(a) Let A be the event that a student reads Hindi newspaper, and B be the event that a student reads English newspaper. We are asked to find P(A' ∩ B'), which is the probability that the student reads neither Hindi nor English newspapers. We can use the formula for the probability of the complement:

P(A' ∩ B') = 1 - P(A ∪ B)

We know that 60% of the students read Hindi newspaper (A), 40% read English newspaper (B), and 20% read both Hindi and English newspapers (A ∩ B). Therefore,

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.6 + 0.4 - 0.2 = 0.8

Substituting this value, we get:

P(A' ∩ B') = 1 - P(A ∪ B) = 1 - 0.8 = 0.2

Therefore, the probability that the student reads neither Hindi nor English newspapers is 0.2.

(b) Let A be the event that a student reads Hindi newspaper, and B be the event that a student reads English newspaper. We are asked to find P(B|A), which is the probability that the student reads English newspaper given that the student reads Hindi newspaper. We can use Bayes' theorem to calculate this:

P(B|A) = P(A ∩ B) / P(A)

We know that 20% of the students read both Hindi and English newspapers (A ∩ B), and 60% of the students read Hindi newspaper (A). Therefore,

P(B|A) = P(A ∩ B) / P(A) = 0.2 / 0.6 = 1/3

Therefore, the probability that the student reads English newspaper given that the student reads Hindi newspaper is 1/3.

(c) Let A be the event that a student reads Hindi newspaper, and B be the event that a student reads English newspaper. We are asked to find P(A|B), which is the probability that the student reads Hindi newspaper given that the student reads English newspaper. We can again use Bayes' theorem:

P(A|B) = P(A ∩ B) / P(B)

We know that 20% of the students read both Hindi and English newspapers (A ∩ B), and 40% of the students read English newspaper (B). Therefore,

P(A|B) = P(A ∩ B) / P(B) = 0.2 / 0.4 = 1/2

Therefore, the probability that the student reads Hindi newspaper given that the student reads English newspaper is 1/2.

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