A bag contains 3 red marbles and 2 blue marbles. A marble is drawn at random and then replaced. A second marble is drawn. Construct a probability tree diagram to represent all possible outcomes.

The tree diagram should have two primary branches representing the first draw: Red (3/5) and Blue (2/5). Each of these branches should then split into two further branches for the second draw, again Red (3/5) and Blue (2/5). The end of each branch should show the combined outcome and its probability (e.g., Red-Red (9/25), Red-Blue (6/25), Blue-Red (6/25), Blue-Blue (4/25)).

A student is taking a multiple-choice quiz with two questions. Each question has 4 possible answers. The student guesses randomly on each question. Draw a probability tree diagram to represent the possible outcomes of the student's guesses (correct or incorrect) on the two questions.

The tree diagram should start with two branches for the first question: Correct (1/4) and Incorrect (3/4). Each of these branches then splits into two further branches for the second question: Correct (1/4) and Incorrect (3/4). The end of each branch shows the combined outcome and probability (e.g., Correct-Correct (1/16), Correct-Incorrect (3/16), Incorrect-Correct (3/16), Incorrect-Incorrect (9/16)).

Probability Tree Diagrams

Grade 10th Grade · Math · 30 min

What's Included

Learning Objective

I can construct and interpret a probability tree diagram to solve probability problems.

Warm-Up Video

Khan Academy · 2:24

Compound events example with tree diagram | Precalculus | Khan Academy

Guided Notes

3 key concepts

1
A tree diagram shows all the possible outcomes of flipping three coins.
2
When flipping three fair coins, there are a total of 8 equally likely outcomes.
3
The probability of getting at least two tails when flipping three fair coins is ½.

Practice Questions

4 questions · Multiple choice & Short answer

Exit Ticket

Quick comprehension check

“Draw a probability tree diagram to represent flipping two fair coins. What is the probability of getting at least one head?”

Complete Lesson Package

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Probability Tree Diagrams

What's Included

Learning Objective

Warm-Up Video

Guided Notes

Practice Questions

Exit Ticket

Complete Lesson Package

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