# 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