Question

in question

a market research group conduct a survey of 1000 consumer and reported that 720 consumer like product a and 450 consumer like product b what is the least number that must have liked both product

why 1000 is taken as u and n(s u t) not taken as 1000

Answer 1

Answer: Given,
Product a liked by consumer = 720
n(a) = 720
Product b liked by consumer = 450
n(b) = 450
Total number of consumer = 1000
n(a $\cup$ b ) = 1000
Least number must have like both n(a $\cap$ b) = ?
We know,
​ n(a $\cup$ b ) = ​n(a) + ​n(b) - ​n(a $\cap$ b)
After substituting all values, we get
1000 = 720 + 450 - ​n(a $\cap$ b)
​n(a $\cap$ b) = 1170 - 1000
= 170 (Ans)