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Compound Events and Counting Methods
Students model multistep chance processes and calculate probabilities using organized lists, trees, tables, and counting rules.
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Beginner
15–20 minutes
Probability & Statistics
Probability & Statistics
Page 6 of 8
Inside Cover
Compound Events and Counting Methods
At a Glance
Binder SectionProbability & Statistics
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
How can a sample space reveal probabilities of compound events?
Build Understanding
A compound event combines two or more events. Use tree diagrams, tables, or organized lists to build the sample space. The multiplication principle counts a sequence of choices.
For independent events, multiply probabilities. For mutually exclusive events, add probabilities. When events overlap, subtract the overlap once. Permutations emphasize order; combinations do not.
Visual Model
4Thousands
3Hundreds
2Tens
7Ones
4,327 = 4,000 + 300 + 20 + 7
Goals
Learning Targets
- Use trees or tables to organize outcomes.
- Independent: P(A and B) = P(A)P(B).
- Mutually exclusive: add probabilities.
- Subtract overlap when events can occur together.
- Order matters in permutations, not combinations.
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Interactive Vocabulary
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Reveal one step at a time
Worked Examples
Example 1
Flip a coin and roll a die
1
12 equally likely ordered outcomes.
2
P(heads and even)=3/12=1/4.
Example 2
Draw two red counters without replacement
1
The second probability changes, so events are dependent.
Ask and explain
Common Questions
Are mutually exclusive events independent? Usually no.
When do I multiply? For successive independent choices or the counting principle.
When does order matter? When different arrangements count as different outcomes.
Notice and correct
Common Misconceptions
Adding probabilities for an “and” event
For independent stages, multiply.
Replacing after a draw without stating it
Replacement determines independence.
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Warm-Up
Guided
Independent
Challenge
1
Quick Start
Warm-Up
Flip two fair coins. Find P(two heads).
2
We Do
Guided Practice
3 shirts and 4 pants make 12 outfits.
Two fair coin flips have 4 equally likely outcomes.
P(two heads) = 1/4.
P(rolling 1 or 2) = 2/6 = 1/3.
Choosing president and vice president is a permutation because roles matter.
3
You Do
Independent Practice
Flip two fair coins. Find P(two heads).
Create and solve a second example with different values.
4
Stretch Your Thinking
Challenge & Real-World Practice
Build a multistage game with a target probability between 0.20 and 0.30. Prove the exact probability and evaluate fairness.
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IXL
Compound Events: Number of Outcomes
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Question 1
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