Question

In a colony,275 families buy TAMIL newspaper ,150families buy ENGLISH newspaper,45 families buy HINDI newspaper,125 families buy TAMIL and ENGLISH newspaper ,17 families buy ENGLISH and HINDI newspaper,5 families buy TAMIL AND HINDI newspaper,3 families buy all the three newspaper if each families by atleast one of the newspaper then find
1.number of families buy ONLY one newspaper
2.number of families buy atlest two newspaper
3.total number of families in the colony

Answer 1

it was a lengthy question , hope this helps

Answer 2

Answer:

Let,

T = event of buying tamil newspaper,

E = event of buying english newspaper,

H = event of buying hindi newspaper,

According to the question,

n(T) = 275,

n(E) = 150,

n(H) = 45,

n(T∩E) = 125,

n(E∩H) = 17,

n(T∩H) = 5,

n(E∩H∩T) = 3,

Thus, the families who buy only Tamil newspaper = n(T) - n(T∩E) - n(T∩H) + n(E∩H∩T)

= 275 - 125 - 5 + 3

= 148

Similarly, who only buy english newspaper = 150 - 125 - 17 + 3

= 11,

Who only buy tamil newspaper = 45 - 17 - 5 + 3 = 26

1. Thus, the number of families buy ONLY one newspaper = 148 + 11 + 26 = 185,

2. Number of families buy at least two newspaper = only T and E + Only E and H + Only H and T + all = n(T∩E) - n(E∩H∩T) + n(E∩H) - n(E∩H∩T) + n(H∩T) - n(E∩H∩T) + n(E∩H∩T)

= 125 - 3 + 17 - 3 + 5 - 3 + 3

= 141

3. total number of families in the colony,

n( T ∪ E ∪ H ) = n(T) + n(E) + n(H) - n(T∩E) - n(E∩H) - n(T∩H) + n(E∩H∩T)

= 275 + 150 + 45 - 125 - 17 - 5 + 3

= 326