Question

In a statistical investigation of 1003 families of Calcutta, it was found that 63 families have neither a radio nor a TV, 794 families have a radio, and 187 have a TV. The number of families having both a radio and a TV is:

• A. \( 41 \)
• B. \( 32 \)
• C. None of these
• D. None of these

Hint:

Use set operations to solve logical counting problems.

Answer 1

The Correct Option is B

Using set theory: \[ n(R) = 794, \quad n(T) = 187, \quad n(R \cup T)' = 63 \] \[ n(Total) = n(R \cup T) + n(R \cup T)' \Rightarrow 1003 = n(R \cup T) + 63 \] \[ n(R \cup T) = 940 \] Using formula: \[ n(R \cup T) = n(R) + n(T) - n(R \cap T) \] \[ 940 = 794 + 187 - n(R \cap T) \] \[ n(R \cap T) = 41 \]