Let H : Set of students reading Hindi newspaper and E : set of students reading English newspaper.
Let n(S) = 100 Then, n(H) = 60
n(E) = 40 and n(H ∩ E) = 20
∴ P(H) = 60/100 = 3/5, P(E) = 40/100 = 2/5 and P(H ∩ E) = 20/100 = 1/5
(i) Required probability = P (student reads neither Hindi nor English newspaper)
= P(H' ∩ E') = P(H ∪ E)' = 1 - P(H ∪ E)
= 1 - [P(H) + P(E) - P(H E)] = 1 - [3/5 + 2/5 - 1/5] = 1 - 4/5 = 1/5
(ii) Required probability = P(a randomly chosen student reads English newspaper, if he/she reads
Hindi newspaper) = P(E/H) = (P(E ∩ H))/P(H) = (1/5)/(3/5) = 1/3
(iii) Required probability = P (student reads Hindi newspaper when it is given that reads English newspaper)
= P(H/E) = (P(H ∩ E))/P(E) = (1/5)/(2/5) = 1/2
