Question 1

Based on the 'Fitness Classes' Venn diagram, how many people are in the universal set $$U$$?

Accepted Answer

$$54 + 34 + 31 + 31 = 150$$

Question 2

In the 'Fitness Classes' diagram, how many people attend only Yoga classes?

Accepted Answer

$$54$$

Question 3

How many people attend both Yoga and Zumba classes according to the 'Fitness Classes' diagram?

Accepted Answer

$$34$$

Question 4

How many people do not attend either Yoga or Zumba classes?

Accepted Answer

$$31$$

Question 5

Using the 'Study Methods' Venn diagram, how many people use only the $$F$$ study method?

Accepted Answer

$$39$$

Question 6

How many people use both $$F$$ and $$G$$ study methods but not $$T$$?

Accepted Answer

$$25$$

Question 7

How many people use all three study methods ($$F$$, $$G$$, and $$T$$)?

Accepted Answer

$$10$$

Question 8

How many people use exactly two study methods according to the 'Study Methods' diagram?

Accepted Answer

$$25 + 18 + 12 = 55$$

Question 9

How many people do not use any of the three study methods ($$F$$, $$G$$, or $$T$$)?

Accepted Answer

$$31$$

Question 10

What is the total number of people represented in the 'Study Methods' Venn diagram?

Accepted Answer

$$39 + 27 + 18 + 25 + 18 + 12 + 10 + 31 = 180$$

Question 11

If a person is chosen at random from the 'Fitness Classes' diagram, what is the probability that they attend at least one class?

Accepted Answer

$$\frac{54 + 34 + 31}{150} = \frac{119}{150}$$

Question 12

In the 'Study Methods' diagram, how many people use $$T$$ but not $$F or$$ $$G$$?

Accepted Answer

$$18$$

Question 13

If a person is chosen at random from the 'Study Methods' diagram, what is the probability that they use exactly one study method?

Accepted Answer

$$\frac{39 + 27 + 18}{180} = \frac{84}{180}$$

Question 14

Suppose a new group is added to the third Venn diagram (currently empty). If 20 people belong to all three sets $$J$$, $$S$$, and $$B$$, how would you represent this in the diagram?

Accepted Answer

Place $$20 in $$the intersection of all three circles.

Question 15

If the universal set $$U in $$the 'Fitness Classes' diagram is increased by 10 people who do not attend any classes, what is the new value for the number outside both circles?

Accepted Answer

$$31 + 10 = 41$$

Question 16

In the 'Study Methods' diagram, how many people use $$G$$ but not $$F or$$ $$T$$?

Accepted Answer

$$27$$

Question 17

If a person is chosen at random from the 'Study Methods' diagram, what is the probability that they use at least two study methods?

Accepted Answer

$$\frac{25 + 18 + 12 + 10}{180} = \frac{65}{180}$$

Venn Diagrams and Set Theory in Liberal Arts Math

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