In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a T.V, 794 families has a radio and 187 has T.V. The number of families in that group

Question

In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a T.V, 794 families has a radio and 187 has T.V. The number of families in that group having both a radio and a T.V is

TestHub · Accepted Answer

Let R be the set of families having a radio and T the set families having a T.V. then n ( R ∪ T ) = The number of families having at least on of the radio and TV = 1003 − 63 = 940 n ( R ) = 794 and n ( T ) = 187 Let x families have both a radio and a T.V. Then number of families who have only radio = 794 − x And the number of families who have only T.V. = 187 − x Erom Venn diagram, 794 − x + x − 187 − x = 940 ⇒ 981 − x = 940 or x = 981 − 940 = 41 Hence, the required number of families having both a radio and a T.V.=41

Mathematics - Sets and Relations Question with Solution | TestHub

Options:

Doubts & Discussion