Question

Market research conducted a survey of 2000 consumers and reported that 1720 consumer like P1 and 1450 consumer like product P2 . what is the least number that must have like the both products?

Answer 1

: Given,

Product a liked by consumer = 1720

n(a) = 1720

Product b liked by consumer = 1450

n(b) = 450

Total number of consumer
= 1000

n(a ∪ b ) = 2000

Least number must have like both n(a ∩ b) = ?

We know,

​ n(a ∪ b ) = ​n(a) + ​n(b) - ​n(a ∩ b)

After substituting all values, we get

2000 = 1720 + 1450 - ​n(a ∩ b)

​n(a ∩ b) = 3170 - 2000

= 1170

Hope this helps!