Question

A survey of 350 collectors showed the following results:

175 collected coins

122 collected comic books

95 collected shot glasses

97 collected coins and comic books

40 collected coins and shot glasses

35 collected comic books and shot glasses

32 collected all three types of items

Based on the above information, fill in the Venn Diagram and then answer the questions below.

1. How many collectors collect comic books or shot glasses?
2. How many collectors collect none of the three types of items?
3. How many collectors collect only coins?
4. How many collectors collect comic books and coins but not shot glasses?
5. How many collectors do not collect shot glasses?

Answer 1

We get the Venn diagram as :

1)

Number of collectors that collect comic books or shot glasses = Number of comic books collected + Number of shot glasses - Number of comic books and shot glasses

= 122 + 95 - 35

= 182

2)

Number of collectors collect none of the three types of items = 350 - Number of collectors that collect coins or comic books or shot glasses

Here we use 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 )

So, we have:

Number of collectors that collect coins or comic books or shot glasses = Number of coins collected + Number of comic books collected + Number of shot glasses collected - Number of coins and comic books collected - Number of coins and shot glasses collected - Number of comic books and shot glasses collected + Number of coins and comic books and shot glasses collected

= 175 + 122 + 95 - 97 - 40 - 35 + 32

= 252

Number of collectors collect none of the three types of items = 350 - 252 = 98

3)

Number of collectors collect only coins = Number of collect coins but not comic books and shot glasses

= Number of coins collected - Number of coins and comic books collected - Number of coins and shot glasses + Number of all three types of items collected

= 175 - 97 - 40 + 32

= 70

4)

Number of collectors collect comic books and coins but not shot glasses = Number of coins and comic books collected - Number of all three types of items collected = 97 - 32 = 65

5)

Number of collectors do not collect shot glasses = 350 - Number of collectors collect shot glasses

= 350 - Number of shot glasses collected

= 350 - 95

= 255