General Addition Rules (Topic 4.6)

Chapter 5 - Day 4

Learning Targets
  • Use a two-way table or Venn diagram to model a random process and calculate probabilities involving two events.

  • Apply the general addition rule to calculate probabilities.

Activity: Can You Taco Tongue and Evil Eyebrow? Day 1
Activity:
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Answer Key:
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Before starting this activity, you might want to start with a discussion about the word “OR”.  Unfortunately, in English “OR” has two possible meanings (Applebees vs. Starbucks “OR”). In mathematics, we want the inclusive Starbucks “OR”.

The first part of this activity is the fun part. Have students work in pairs. Each student needs to decide if their partner is a "Yes" or "No" for Taco Tongue and a "Yes" or "No" for Evil Eyebrow. Students then go to the front whiteboard to record the data by recording a tally mark for themselves in the correct part of the two-way table. 

Pro Tip: Students may get confused about how the two-way table works. They often think they need to put two tally marks on the board (one for Taco Tongue and one for Evil Eyebrow). Inform them that they are each only putting 1 tally mark on the board and their are four possibilities (Yes/Yes, Yes/No, No/Yes, and No/No). 

Once the data have been collected, students can work in pairs/groups to complete the rest of the activity. 

Debrief

Make sure to point out the close connection between the two-way table and the Venn Diagram (after all, they are totally BFFs). You can also use this example to define the 4 regions of a Venn Diagram: left pacman, the football, the right pacman, and the outside.

When you get to question #3, give students a visual representation of the probabilities:

  • "If you are Yes Evil Eyebrow, please stand up." Count them out loud then have them sit.

  • "If you are No Evil Eyebrow, please stand up." Count them out loud then have them sit.

  • "If you are Yes Evil Eyebrow OR No Evil Eyebrow, please stand up." Count them out loud then have them sit.

No problem here. We could have simply added the counts from the first two groups.


When you get to question #4, give students a visual representation of the probabilities:

 

  • "If you are Yes Taco Tongue, please stand up." Count them out loud then have them sit.

  • "If you are Yes Evil Eyebrow, please stand up." Count them out loud then have them sit.

  • "If you are Yes Taco Tongue OR Yes Evil Eyebrow, please stand up." Count them out loud then have them sit.


Big problem here. We can't simply add the counts from the first two groups. Why not? Because some people were double counted! Call out the names of the students that were double counted and have them stand. Subtract them out and you will arrive at the correct answer. The purpose of this activity is to get students thinking and reasoning about the General Addition Formula, rather than just memorizing a formula (Experience First, Formalize Later).

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