Question

in a group of 60 people 27 liked cold drink 42 like hot drinks and each person like at least one of the two drinks how many like both hot and cold drinks​

Answer 1

Answer:

Let A = Set of people who like cold drink

And, B = Set of people who like hot drink

Given,

n(A∪B)=60

n(A)=27 and n(B)=42

n(A∩B)=n(A)+n(B)−n(A∪B)

n(A∩B)=27+42−60=9

Therefore, 9 people like both cold drink and hot drink.

Answer 2

Answer:

1. Using formula: n(AUB) = n(A) + n(B) - n(A intersection B)
2. Given: n(AUB) = 60 , n(A) = 27 , n(B) = 42 , n(A intersection B) = ?
3. 60 = 27 + 42 - n(A intersection B)
4. 60 = 69 - n(A intersection B)
5. n(A intersection B) = 69 - 60 = 9.

Step-by-step explanation:

Firstly, We need to learn the formula and never forget it.

Secondly, 60 is the number of people in a group, therefore n(AUB) is 60.

Thrirdly, 27 is the number of people who liked the cold drink, therefore n(A) is 27.

fourthly, 42 is the number of people who liked hot drinks.

Lastly, Remember: at least or either trying to say both.

Here's another tip: if you ever see like this question and you see at least or either, remember; the question is trying to ask you to find n(A intersection B) and if you want n(A) to be 42 and n(B) 27 it's all correct.

As you see, in number 3; I was applying the formula.

In 4, 27 plus 42 is 69 as you see here.

And therefore I change the sides: n(A intersection B) on the left and 60 on the right and becomes negative. And, n(A intersection B) is now positive. You got n(A intersection B) = 69 - 60 = 9.

Therefore, 9 people liked both hot and cold drinks.