General Multiplication Rule (Lesson 5.5)

Chapter 5 - Day 6

Learning Targets
  • Use the general multiplication rule to calculate probabilities.

  • Use a tree diagram to model a chance process involving a sequence of outcomes.

  • Calculate conditional probabilities using tree diagrams.

Activity: Can You Get a Pair of Aces or Pair of Kings?
Activity:
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Experience First

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.

 

As students are working through the tree diagram in the activity, encourage them to have the five cards face up in front of them on their desk. This makes the second column of probabilities in the tree diagram (the conditional probabilities) much easier to find. For example, to find the P(2nd Ace | 1st Ace) simply remove the 1st ace and the answer is remaining right in front of you (1 out of 4).

Formalize Later

Be sure that students know that the second column of probabilities in the tree diagram are conditional probabilities. For example, the top value 1/4 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 (like the last question in the activity), but it is much easier to think and reason your way to an answer using the tree diagram.

 

We always have students calculate all 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.