Advertisement Remove all ads

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 - Mathematics and Statistics

Sum

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.
Advertisement Remove all ads

Solution

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.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×