In a hostel, 60% of the students read Hindi news paper, 40% read Engli

1.	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» 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

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»

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