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 newspapers.

Answer 1

The probability that a student in the hostel reads neither Hindi nor English newspapers is 20%.

Step-by-step explanation:

To find the probability that a student reads neither Hindi nor English newspapers, we can use the principle of inclusion-exclusion for two sets. The principle states:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Where P(A) is the probability that a student reads a Hindi newspaper, P(B) is the probability that a student reads an English newspaper, and P(A ∩ B) is the probability that a student reads both newspapers. Now using the given percentages, we can convert them into probabilities:

Plug the values into the inclusion-exclusion principle:

P(A ∪ B) = 0.60 + 0.40 - 0.20 = 0.80

The probability that a student reads either Hindi or English newspapers is 0.80 (or 80%). To find the probability that a student reads neither, we subtract this from 1 (the total probability space):

P(neither) = 1 - P(A ∪ B) = 1 - 0.80 = 0.20

Thus, the probability that a student reads neither Hindi nor English newspapers is 0.20 or 20%.