Question

In a party 50 people 44% like to drink coffee 46% like to drink tea and rest prefer soft drinks. Find the number of person who like soft drinks.​

Answer 1

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T = Tea

C = Coffee

n means number

n(T) = 30

n(C) = 20

Universal = 50

n(T U C)' = 6 , T union C complement (people who like to drink neither)

Let n(T Π C) i.e. T intersection C (People who like to drink both) = x

$n(T) + n(C) - n(T Π C) + n(T U C)' = 50$

$30 + 20 - x + 6 = 50$

$56 - x = 50$

$- x = 50 - 56$

$-x = -6$

$x = 6$

Therefore people who like to drink BOTH Tea and Coffee are 6.

People who drink coffee = 20

Thus, People who ONLY drink coffee = 20 - 6 = 14 people

I've attached an image with diagram below for better understanding.

and look at the pic

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Answer 2

Answer:

T = Tea

C = Coffee

n means number

n(T) = 30

n(C) = 20

Universal = 50

n(T U C)' = 6 , T union C complement (people who like to drink neither)

Let n(T Π C) i.e. T intersection C (People who like to drink both) = x

n(T) + n(C) - n(T Π C) + n(T U C)' = 50n(T)+n(C)−n(TΠC)+n(TUC)

'

=50

30 + 20 - x + 6 = 5030+20−x+6=50

56 - x = 5056−x=50

- x = 50 - 56−x=50−56

-x = -6−x=−6

x = 6x=6

Therefore people who like to drink BOTH Tea and Coffee are 6.

People who drink coffee = 20

Thus, People who ONLY drink coffee = 20 - 6 = 14 people