Zachariah Norris

2022-09-25

A problem of Set Theory The question is :
In a market survey,a manufacturer obtained the following data :
Did you use our brand? Percentage answering yes
1. April 59
2. May 62
3. June 62
4. April and May 35
5. May and June 33
6. April and June 31
7. April,May and June 22
Is this correct?

Chiecrere2f

This is not correct, and we can see this using only statements 1, 2, and 4.
Let A = # of people who responded to the survey in April, M = # of people who responded to the survey in May.
Then A + M = total # of people who responded in April and May.
By (1), (0.59)*A = # of people who answered yes in April and by (2), (0.62)*M = # of people who answered yes in May.
If we add these values, we get # of people who answered yes in April and May, which by (4) is equal to (0.35)*(A + M)
So we get the equation (0.59)*A + (0.62)M = (0.35)(A + M)
Solve for A and get A = -(0.27/0.24)*M
This suggests that A = M = 0, or that one of A and M is negative. Both of these cases are impossible for a survey of people, for # of people is a strictly positive quantity.

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