Question

In a statistical investigation of $1,003$ families of Calcutta, it was found that $63$ families had neither a radio nor a T.V, $794$ families had a radio and $187$ had a T.V. The number of families in that group having both a radio and a T.V is

• A. $36$
• B. $41$
• C. $32$
• D. None of these

Answer 1

Answer: (B)

$41$

Total $=1003$

Let $TV$ Be set $A$ and radio be

set $B$

$n\left(A\right)=187$ $n\left(B\right)=794$

$n(\overline{A}\cap \overline{B})=63$

$\therefore n(A\cup B)=1003-63$

$=940$

$n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$940=187+794-n(A\cap B)$

$n(A\cap B)=981-940$

$n(A\cap B)=41$

$41$ families have both