Question

From amongst 2000 literate individuals of a town, 70% read Marathi newspapers, 50% read English newspapers and 32.5% read both Marathi and English newspapers. Find the number of individuals who read.

1. at least one of the newspapers.
2. neither Marathi nor English newspaper.
3. Only one of the newspapers.

Answer 1

Let M = set of individuals who read Marathi newspapers

E = set of individuals who read English newspapers

X = set of all literate individuals

∴ n(X) = 2000,

n(M) = `70/100 xx 2000` = 1400

n(E) = `50/100 xx 2000 = 1000`

n(M ∩ E) = `32.5/100 xx 2000 = 650`

n(M ∪ E) = n(M) + n(E) - n(M ∩ E)

= 1400 + 1000 - 650

= 1750

(i) No. of individuals who read at least one of the newspapers

= n(M ∪ E) = 1750

(ii) No. of individuals who read neither Marathi nor English newspaper

= n(M' ∩ E')

= n(M ∪ E)'

= n(X) - n(M ∪ E)

= 2000 - 1750

= 250

(iii) No. of individuals who read only one of the newspapers = n(M ∩ E') + n(M' ∩ E)
= n(M ∪ E) – n(M ∩ E)

= 1750 – 650

= 1100