Question

3. In a survey of 600 consumers, it was found that 400
purchase Mechi Tea, 250 purchase Tokla Tea and
150 purchase both brands. How many consumers
purchase neither of these brands?​

Answer 1

Answer:

Step-by-step explanation:

250 people

Answer 2

The number of consumers who purchase neither of these brands = 100

Given :

In a survey of 600 consumers, it was found that 400 purchase Mechi Tea, 250 purchase Tokla Tea and 150 purchase both brands

To find :

The number of consumers who purchase neither of these brands

Solution :

Step 1 of 2 :

Calculate the number of consumers who purchase Mechi Tea or Tokla Tea

Let ,

S = Set of all consumers

A = Set of all consumers who purchase Mechi Tea

B = Set of all consumers who purchase Tokla Tea

Then by the given ,

n(S) = 600 , n(A) = 400 , n(B) = 250 , n(A ∩ B) = 150

We know that ,

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

⇒ n(A ∪ B) = 400 + 250 - 150

⇒ n(A ∪ B) = 500

∴ The number of consumers who purchase Mechi Tea or Tokla Tea = 500

Step 2 of 2 :

Calculate number of consumers who purchase neither of these brands

The number of consumers who purchase neither of these brands

$\displaystyle \sf{ = n( \bar{A} \: \cap \: \bar{B})}$

= n(S) - n(A ∪ B)

= 600 - 500

= 100

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