Algebra 2 Honors Lesson

The Addition Rule: P(A or B) and Mutually Exclusive Events

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10-11BTC Style / Thinking Classrooms12-190 min

Learning Objective

Students will apply the Addition Rule to calculate P(A or B) for both overlapping and mutually exclusive events, and distinguish between the two cases.

Lesson Overview

Students progress from identifying overlapping vs. mutually exclusive events using Venn diagrams, to applying the Addition Rule P(A or B) = P(A) + P(B) − P(A and B), to solving multi-step probability problems in context. The sequence changes one variable at a time, building from concrete set notation to algebraic reasoning.

Materials

Vertical whiteboards or chart paper
Dry-erase markers (multiple colors)
Printed Venn diagram templates (blank, two overlapping circles)
Printed Four-Quadrant consolidation note sheets
Basic calculators
Colored markers or highlighters for shading Venn diagram regions

Scaffolded Task Progression

1Task 1

A standard six-sided die is rolled once. The sample space is

{1, 2, 3, 4, 5, 6}

.

Let

A = {2, 4, 6}

and

B = {5, 6}

.

1. List all outcomes in event

A

.
2. List all outcomes in event

B

.
3. List all outcomes that are in both

A

and

B

.
4. Are there any outcomes in both events? What does that tell you about

A

and

B

2Task 2

Using the same die and the same events A = {2, 4, 6} and B = {5, 6}:

1. What is

P (A)

?
2. What is

P (B)

?
3. What is

P (A and B)

?
4. What is

P (A) + P (B)

? What is wrong with using this as

P (A or B)

3Task 3

Still using the same die, events A = {2, 4, 6} and B = {5, 6}.

Using the Addition Rule:

P (A or B) = P (A) + P (B) - P (A and B)

1. Substitute the values you found in Task 2.
2. Calculate

P (A or B)

.
3. Verify by listing all outcomes in 'A or B' directly and counting them.

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