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
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