A pollster interviewed 500 university seniors who owned credit cards. She reported that 240 had Goldcard, 290 had Supercard, and 270 had Thriftcard.

Question

Of those seniors, the report said that:
80 owned only a Goldcard and a Supercard,
70 owned only a Goldcard and a Thriftcard,
60 owned only a Supercard and a Thriftcard, and
50 owned all three cards.

When the report was submitted for publication in the local campus newspaper, the editor refused to publish it, claiming the poll was not accurate. Was the editor right? Why or why not?

Answer 1

The editor was right. The numbers add up to more than 500.

Answer 2

Using the formula ...
n(A or B or C)
= n(A) + n(B) + n(C) - n(A and B) - n(A and C) - n(B and C) + n(A and B and C)

500 = 240 + 290 + 270 - 80 - 70 - 60 + 50
500 = 640

not true, so data not consistent.

You could also make Venn diagrams to show the data distribution.