# Can You Taco Tongue and Evil Eyebrow? Two Lessons for Teaching Probability

Probability is so boring. Let's see if we can change that.

**LEARNING TARGETS - DAY 1**

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.

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____).__

**LEARNING TARGETS - DAY 2**

Calculate and interpret conditional probabilities.

Determine if two events are independent.

In this activity, students will use the data collected from Day 1. This is a two-page activity and you will want to have students **pause at the end of page 1 for a full class debrief** before moving to page 2.

Notice how this lesson progresses from informal to formal. On the first page, students are calculating conditional probabilities (without knowing this term) and thinking about independence without any formulas. On the second page, we use formal probability notation and eventually arrive at a formula for checking independence.

**How Do I Get Students to Fill in the INDEPENDENT table?
**

**Teacher: "What percent of all EKHS Senior are Yes Taco Tongue?"**

Student answer: 480/600 = 80%

**Teacher: "So if Taco Tongue and Evil Eyebrow are independent, what percent of the Yes Evil Eyebrows should be Yes Taco Tongue?"**

Student answer: 80%

**Teacher: "So how many is this?"**

Student answer: 80% of 200 = 160

**Teacher: "Now fill in the rest"**