Conditional Probability and Tree Diagrams
Day 49 - Lesson 5.3
Use the general multiplication rule to calculate probabilities.
Use a tree diagram to model a chance process involving a sequence of outcomes and to calculate probabilities.
When appropriate, use the multiplication rule for independent events to calculate probabilities.
Activity: Can you get a pair of Aces or a pair of Kings
To spark interest in today’s activity, play the game in front of the class with a few students and offer prizes (candy bars always work). Then pose this thought to the class “I wonder what the probability of winning this game would be?” After they roll their eyes, students will be ready for the activity.
Tips for tree diagrams
We always have students calculate all of the probabilities at the end of the tree diagram, even if they aren’t all needed to answer the question. Then they can check that all of the probabilities add to 1, allowing them to go back and fix a mistake if they made one.
Be sure that students know that the second column of probabilities in the tree diagram are conditional probabilities. For example, the top value is P(2nd card Ace | 1st card Ace). Students will often misunderstand this value as P(1st card Ace AND 2nd card Ace), which is actually the probability in the far right of the tree diagram.
A tree diagram is a strategy for solving probability questions that allows students to avoid the dangers of FORMULAS! Yes the questions in the activity could all be solved with formulas, but students often make mistakes in this process (especially with conditional probabilities!).