Question

From a survey. 73% like coffee. 65% like tea. and 55% like both coffee and tea then how many person do not like both tea and coffee.

Answer 1

number of people like coffee equals to 73 percentage number of people liked equals to 65 percentage people like both coffee and tea equals to 55 percentage

Answer 2

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FORMULA TO BE IMPLEMENTED

$n(C \cup \: T) = n(C) + n(T) - n(C \cap \: T)$

QUESTION

From a survey 73% like coffee 65% like tea and 55% like both coffee and tea

TO DETERMINE

The number of person do not like both tea and coffee

ANSWER

Let

C = The set of people who like coffee

T = The set of people who like tea

U = Universal Set

Then

$\displaystyle \: n(C) = \frac{73}{100}$

$\displaystyle \: n(T) = \frac{65}{100} \:$

$\displaystyle \: n(C \cap \: T) = \frac{55}{100} \:$

$\displaystyle \: n(U) = 1$

We know that

$n(C \cup \: T) = n(C) + n(T) - n(C \cap \: T)$

$\displaystyle \: \implies \: n(C \cup \: T) = \frac{73}{100} + \frac{65}{100} - \frac{55}{100}$

$\displaystyle \: \implies \: n(C \cup \: T) = \frac{83}{100}$

So

$\displaystyle \: \: n({C}^{c} \cap \: {T}^{c} )$

$= \displaystyle \: n(U) - \: n(C \cup \: T)$

$= \displaystyle \: 1 - \frac{83}{100}$

$= \displaystyle \: \frac{17}{100}$

RESULT

The number of person do not like both tea and coffee 17 %