A survey of 500 television watchers produced the following information:

285 watch football games, 195 watch hockey games, 115 watch basketball games, 4 watch football and basketball games, 70 watch football and hockey games, 50 watch basketball and hockey games. 50 do not watch any three kinds of games. Find:

i) How many in the survey watch all 3 kinds of games?

ii) How many watch exactly one of the sports languages?

iii) Draw Venn Diagram showing results of the survey.

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 8 Marks

Year: May 2015

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