# Lesson Worksheet: Set Notation Mathematics

In this worksheet, we will practice using set notation with Venn diagrams and calculate probabilities using Venn diagrams.

**Q1: **

A bag contains an unknown number of red, blue, green, red and blue, and green and blue balls. We name the events of choosing a ball containing each color , , and . Given that , , , and and that there are 12 balls containing blue in the bag, determine the total number of balls in the bag and .

- A40, 0.3
- B20, 0.6
- C40, 0.6
- D20, 0.3
- E60, 0.2

**Q2: **

Given that , , and , calculate .

**Q3: **

Given that and , calculate .

**Q4: **

Which of the following represents the colored area in the Venn diagram in set notation?

- A
- B
- C
- D
- E

**Q5: **

Which of these Venn diagrams has the set as a colored area?

- A
- B
- C
- D
- E

**Q6: **

In a group of 10 people, the probability a chosen person likes cats is given by and the probability they like dogs is given by . Given that and that no one in the group dislikes both cats and dogs, find the size of the set .

**Q7: **

Which of these Venn diagrams has the set as a colored area?

- A
- B
- C
- D
- E

**Q8: **

Given that , , , , , , and , determine if and are mutually exclusive events.

- AYes, they are mutually exclusive.
- BNo, they are not mutually exclusive.

**Q9: **

The probability that a person likes carrots is 0.5, the probability that a person likes parsnips is 0.4, and the probability that a person likes both is 0.1. Find .

**Q10: **

A biased 20-sided die is rolled twenty times.

Let denote the event that an even number is rolled and denote the event that a number greater than 15 is rolled. The following Venn diagram shows the numbers of each event that were rolled.

Use the diagram to estimate the probability .

- A
- B
- C
- D
- E