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

Step-by-step solution

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 T V =1003-63=940n( 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