Question

Q.NO.6: 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 three

games. How many watch all the three games? How many watch

exactly one of the three games?

Answer 1

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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