1 A survey of 500 television viewers produced the given information;285 watch football;195 watch hockey;115 watch cricket;70 watch football and - Maths - Sets

Question

1 A survey of 500 television viewers produced the given
information;285 watch football;195 watch hockey;115 watch
cricket;70 watch football and hockey;45 watch football and cricket
;50 do not watch any of three games How many watch exactly one of
the three games ?

Ajanta Trivedi · Accepted Answer

if your query is:

A survey of 500 television viewers produced the given information;285 watch football;195 watch hockey;115 watch cricket;70 watch football and hockey;45 watch football and cricket ;50 watch cricket and hockey;50 do not watch any of three games.How many watch exactly one of the three games.

Let A, B and C represents the number of viewers, who watched football , hockey and cricket respectively.

therefore

$| A | = 285, | B | = 195, | C | = 115 | A \cap B | = 70, | A \cap C | = 45, | B \cap C | = 50 | A \cup B \cup C | = 500 - 50 = 450$ [since 50 do not watch any of the three games ]

those who watch all the three games

$| A \cap B \cap C | = | A \cup B \cup C | - {| A | + | B | + | C |} + | A \cap B | + | B \cap C | + | B \cap C | = 450 - {285 + 195 + 115} + 70 + 45 + 50 = 450 - {595} + 165 = 615 - 595 = 20$

the number of viewers who watched only football

$| A - B - C | = | A | - [| A \cap B | + | A \cap C |] + | A \cap B \cap C | = 285 - [70 + 45] + 20 = 305 - 115 = 190$

the number of viewers who watched only hockey

$| B - A - C | = | B | - [| A \cap B | + | B \cap C |] + | A \cap B \cap C | = 195 - [70 + 50] + 20 = 215 - 120 = 95$

the number of viewers who watched only cricket

$| C - A - B | = | C | - [| A \cap C | + | B \cap C |] + | A \cap B \cap C | = 115 - [45 + 50] + 20 = 135 - 95 = 40$

therefore the number of viewers who watched exactly one game

=190+95+40

=325

hope this helps you.

cheers!!

1.A survey of 500 television viewers produced the given information;285 watch football;195 watch hockey;115 watch cricket;70 watch football and hockey;45 watch football and cricket ;50 do not watch any of three games.How many watch exactly one of the three games ?