Lesson Worksheet: Set Notation Mathematics

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


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 R, G, and B. Given that 𝑃()=0.2R, 𝑃()=0.1RB, 𝑃()=0.5G, and 𝑃()=0.2GB and that there are 12 balls containing blue in the bag, determine the total number of balls in the bag and 𝑃()B.

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


Given that 𝑃(𝐴)=0.6, 𝑃(𝐵)=0.35, and 𝑃(𝐴𝐵)=0.25, calculate 𝑃𝐴𝐵.


Given that 𝑃(𝐴)=0.55𝑃(𝐴𝐵)=0.8 and 𝑃(𝐴𝐵)=0.2, calculate 𝑃(𝐵).


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

  • A𝐴𝐵
  • B𝐴𝐵
  • C𝐴𝐵
  • D𝐴𝐵
  • E𝐴𝐵


Which of these Venn diagrams has the set (𝐴𝐵)𝐶 as a colored area?

  • A
  • B
  • C
  • D
  • E


In a group of 10 people, the probability a chosen person likes cats is given by 𝑃(𝐶)=0.6 and the probability they like dogs is given by 𝑃(𝐷)=0.5. Given that 𝑃(𝐶𝐷)=0.4 and that no one in the group dislikes both cats and dogs, find the size of the set 𝐶𝐷.


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

  • A
  • B
  • C
  • D
  • E


Given that 𝑃(𝐴)=0.4, 𝑃(𝐵)=0.25, 𝑃(𝐶)=0.75, 𝑃(𝐴𝐵)=0.15, 𝑃(𝐴𝐶)=0.15, 𝑃(𝐴𝐵𝐶)=0.1, and 𝐴𝐵𝐶=, determine if 𝐴 and 𝐶 are mutually exclusive events.

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


The probability that a person likes carrots (𝐶) is 0.5, the probability that a person likes parsnips (𝑃) is 0.4, and the probability that a person likes both is 0.1. Find 𝑃(𝐶𝑃).


A biased 20-sided die is rolled twenty times.

Let 𝐸 denote the event that an even number is rolled and 𝐺 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 𝑃(𝐸𝐺).

  • A1320
  • B910
  • C12
  • D720
  • E120

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