Question

A survey of 500 television viewers produced the following information; 285 watch football, 195 watch hockey, 115 watch basketball, 45 watch football and basketball, 70 watch football and hockey, 50 watch hockey and basketball, 50 do not watch any one of three games ?

Answer 1

Total number of viewers of television $=500$

$n\left(F\right)=285$

$n\left(H\right)=195$

$n\left(B\right)=115$

$n(F\cap B)=45$

$n(B\cap H)=50$

$n(H\cap F)=70$

Viewers watch all three games$=500-50=450$

$\because n(F\cup B\cup H)=n\left(F\right)+n\left(B\right)+n\left(H\right)-n(F\cap B)-n(B\cap H)-n(H\cap F)+n(F\cap B\cap H)$

$450=285+195+112-70-50-45+n(F\cap B\cap H)$

$450-430=n(F\cap B\cap H)$

$n(F\cap B\cap H)=20$