# A company studies the product preferences of 20,000 consumers. It was found that each

#### DAVV MBA PYQ

A company studies the product preferences of 20,000 consumers. It was found that each of the products A, B and C was liked by 7020, 6230 and 5980 respectively. All products were liked by 1500. Products A and B were liked by 2580, products A and C were liked by 1200 and products B and C were liked by 1950. Prove that the study results are not correct.
Solution:

Formula:
n(A U B U C) = n(A)+n(B)+n(C)-n(A ∩ B)-n(A ∩ C)-n(B ∩ C)+n(A ∩ B ∩ C)
Given,
n(A U B U C) = 20000
n(A) = 7020
n(B) = 6230
n(C) = 5980
n(A ∩ B ∩ C) = 1500
n(A ∩ B) = 2580
n(A ∩ C) = 1200
n(B ∩ C) = 1950
n(A U B U C) = 7020+6230+5980-2580-1200-1950+1500 = 15000
But, given n(A U B U C) = 20000,
So result is not correct.
n(A U B U C) ≠ 15000
Video Explanation

#### Practice questions (DAVV MBA PYQs):

Q1. In a city there are 100000 people, 64% of them speak Greek, 55% people speak Latin, 43% people speak French, 21% people speak both Greek and Latin, 31% people speak both Greek and French, and 41% people speak both Latin and French. Determine the number of people speak all the three languages.