(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.
