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 ?

Answer 1

315 people exactly watch one of the three games

Answer 2

Answer:

Step-by-step explanation:

Let F denote people watch football.

H denotes people watch hockey.

B denotes people watch basketball.

Now,

|F|=285

|H|=195

|B|=115

|FՈH| =70

|FՈB| =45

|HՈB| =50

(|F U H U B|)'=50

|F Ո H Ո B| = |F U H U B|-|F|-|H|-|B|+| F Ո H |+| H Ո B |+|F Ո B| =20

Hence, 20 viewers watch all 3 kinds of games.

|F – H- B|=|F| - | F Ո H |-| F Ո B |+| F Ո H Ո B |=190

|H – B - F|=95

|B – F - H|=40

Hence, No of viewers who watch exactly one of the sports = 190+95+40 = 325

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