- StatisticsToggle Dropdown
- Why Study Statistics?
- Descriptive & Inferential Statistics
- Fundamental Elements of Statistics
- Quantitative and Qualitative Data
- Measurement Data Levels
- Collecting Data
- Ethics in Statistics
- Describing Qualitative Data
- Describing Quantitative Data
- Histograms
- Stem-and-Leaf Plots
- Measures of Central Tendency
- Measures of Variability
- Describing Data using the Mean and Standard Deviation
- Measures of Position
- Z-Scores

- Probability
- Inferential StatisticsToggle Dropdown

Two sets are known to be **mutually exclusive **when they have no common elements.

Consider the set of all even positive integers, and the set of all odd positive integers:

Set A = {\( 2, 4, 6, 8, 10, 12, 14, 16... \)}

Set B = {\( 1, 3, 5, 7, 9, 11, 13, 15... \)}

We call them **mutually exclusive **since none of the elements of Set A are in Set B, and vice versa.

Recall that an event is a **set of outcomes** from Simple and Compound Events. It follows that **mutually exclusive events **are those that do not share any of the same outcomes.

*How do we calculate the probability of these events? Let us visualize using a Venn Diagram:*

If \( A \) and \( B \) are two mutually exclusive events, then the probability of \(A \) **or **\( B \) occurring is their respective probabilities added together.

Two sets are **non-mutually exclusive **if they share common elements.

Consider the set of all numbers from 1 to 10, and the set of all even numbers from 1 to 16:

Set A = {\( 2, 4, 6, 8, 10, 12, 14, 16 \)}

Set B = {\( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \)}

We call them **non-mutually exclusive **since they share the common elements of \( 2, 4, 6 \) and \( 8 \).

It follows that two events are **non-mutually exclusive **if they share common outcomes.

*How do we calculate the probability of these events? Let us visualize using another Venn Diagram:*

If \( A \) and \( B \) are two non-mutually exclusive events, then the probability of \( A \) **or **\(B \) occuring is both of their probabilities added together and subtracting the probability of **both **of them occurring.

__EXAMPLE __

a) A box contains 2 red, 4 green, 5 blue and 3 yellow marbles. If a single random marble is chosen from the box, what is the probability that it is red or green marble?

b) In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5 girls made an A grade. If a student is chosen at random from the class, what is the probability of choosing a girl or an A student?

See the video below for the solution:

- Last Updated: Apr 20, 2023 12:47 PM
- URL: https://libraryguides.centennialcollege.ca/c.php?g=717168
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