Question

In a hostel, 60% of the students read Hindi news paper, 40% read English news paper and 20% read both Hindi and English news papers. A student is selected at random. (a) Find the probability that she reads neither Hindi nor English news papers. (b) If she reads Hindi news paper, find the probability that she reads English news paper. (c) If she reads English news paper, find the probability that she reads Hindi news paper.

Answer 1

(a) 40%
(b)20%
(c)20%......

Answer 2

Hey !!

Let A be the event that a student reads Hindi newspaper and B be the event that a student reads English Newspaper.

P(A)  = $\frac{60}{100} = 0.6 , P(B) = \frac{40}{100}$

And P (A ∩ B) = $\frac{20}{100} = 0.2$

(a) Now  P (A ∪ B) = P(A) + P(B) - P(A ∩ B)

           = 0.6 + 0.4 - 0.2 = 0.8

Probability that she reads neither Hindi nor English newspaper

             = 1 - P(A ∪ B) = 1 - 0.8 = 0.2 = $\frac{1}{5}$

(b) P(B/A) = P(A ∩ B) / P (A) = $\frac{0.2}{0.6} = \frac{1}{3}$

(c) P (A/B) = P (A ∩ B) / P(B) = $\frac{0.2}{0.4} = \frac{1}{2}$

GOOD LUCK !!