Independent and Dependent Events
Chapter 5 - Day 6 - Lesson 5.3
Use a two-way table or Venn diagram to model a chance process and calculate probabilities involving two events (from Lesson 5.2).
Calculate and interpret conditional probabilities.
Determine if two events are independent.
There is some review from Lesson 5.2 on the the first page of this activity. The rest of the activity is aimed at getting students to understand the concept of independence (NOT A FORMULA!).
Two-way tables and Venn diagrams
Because this two-way table is 2 X 2, it is a great example to show students the close connection between a two-way table and a 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.
How to check for independence:
Use a memorized formula.
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.
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 “Female” has occurred and see what happens to the probability of “English”. In other words, see if this formula holds true.
If these two probabilities are equal, then knowing whether or not the person is female does not change the probability that the person prefers English. 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!).