According to a survey of $500$ people, $300$ preferred tea while $100$ preferred coffee. $50$ people preferred both tea and coffee. how many people didn't prefer any of the drinks?

350

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150

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400

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None of the above

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Solution

The correct option is B $150$
Let, $T$ be the set of people who preferred Tea and $C$ be the set of people who preferred Coffee.

Given : $n (T) = 300, n (C) = 100, n (T \cap C) = 50 a n d n (U) = 500$
To find : No. of people who do not prefer any of drink $= n (T \cap C)^{'}$

We know,
$n (T \cup C) = n (T) + n (C) - n (T \cap C)$
So, $n (T \cup C) = 300 + 100 - 50$
$= 350$
We also know,
$n (T \cup C) + n (T \cup C)^{'} = n (U)$
$n (T \cup C)^{'} = 500 - 350$
$= 150$

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According to a survey of 500 people, 300 preferred tea while 100 preferred coffee. 50 people preferred both tea and coffee. how many people didn't prefer any of the drinks?

According to a survey of $500$ people, $300$ preferred tea while $100$ preferred coffee. $50$ people preferred both tea and coffee. how many people didn't prefer any of the drinks?