Question

In the Venn Diagram given below, A represents the total number of people in a town who like cricket = 1300. B represents the total number of people who like badminton = 500 and C represents the total number of people who like Tennis = 100. If AB = 9, BC = 12, AC = 13 and ABC = 2, how many people like only one game?

Answer 1

Concept Introduction: Venn Diagrams give a good idea of a topic.

Given:

We have been Given: Total who like Cricket,

$a = 1300$

Total who like Badminton,

$b = 500$

Total who like Tennis,

$c = 100$

$ab = 9 \\ bc = 12 \\ ac = 13 \\ abc = 2$

To Find:

We have to Find: how many people like only one game?

Solution:

According to the problem, To find people who like only one game we will do,

$people \: like \: one \: game = total \: people - total \: people \: like \: more \: than \: one \: game$

therefore putting the values, we get,

$= (1300 + 500 + 100) - (9 + 12 + 13 + 2) \\ = 1900 - 36 \\ = 1864$

Final Answer: The no. of people liking only one game is

$1864 \: people$

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Answer 2

Answer:

1864 people in the town like only 1 game out of the three mentioned.

Step-by-step explanation:

Like we have learnt, Venn diagrams are a part of the pictorial representation of the vast branch of statistics. They give us a very detailed visual representation of any given data.

Here, we are given the following data.

A = total people who like cricket = 1300

B = total people who like badminton = 500

C = total people who like tennis = 100

AB = 9

BC = 12

AC = 13

ABC = 2

We need to find the number of people who like only 1 game.

To do this, we use the logical formula which is

The no. of people who like 1 game = total no. of people - total no. of people who like more than 1 game

By substituting the values in the given formula, we get

$N = (1300 + 100 + 500) - (9 + 12 +2 +13)\\N = 1900 - 36\\N = 1864$

Thus, we have found out that 1864 people in the town like only 1 game out of the 3 mentioned.

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