Independent and Dependent Events (Topic 4.6)

Chapter 5 - Day 6

Learning Targets
  • Use a two-way table or Venn diagram to model a random process and calculate probabilities involving two events (from Lesson 5.2).

  • Calculate and interpret conditional probabilities.

  • Determine whether two events are independent.

Activity: Can You Taco Tongue and Evil Eyebrow? Day 2
Answer Key:

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"

How to check for independence:

Old school:

Use a memorized formula.

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Calculate all three of these probabilities from the table, plug them into the formula, and see if it holds true. The problem here is that there is no real fundamental understanding of independent events utilized in this approach.


New school:

Start with the concept of independent events: A and B are independent events if knowing whether or not one event has occurred does not change the probability that the other event will happen.

Let’s consider both cases of whether or not “Evil Eyebrow” has occurred and see what happens to the probability of “Taco Tongue”.  In other words, see if this formula holds true.

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If these two probabilities are equal, then knowing whether or not the person can Evil Eyebrow does not change the probability that the person can Taco Tongue. The two events are independent!

We prefer the New School approach because it relies on a fundamental understanding of independent events (and NOT A MEMORIZED FORMULA!).