Lesson 4: 5.4 Conditional Probability and Independence
Duration of Days: 3
Lesson Objective
Students will be able to calculate and interpret conditional probabilities and use the multiplication rule to determine if two events are independent.
1. How does the "denominator" change when we are given a piece of information (e.g., "Given the student is a girl...")?
2. How do we mathematically prove that knowing one event happened provides "zero information" about the other event?
Conditional probability
Independent events
General Multiplication Rule
Tree diagram
HSS-CP.A.3: Understand the conditional probability of A given B as P(A and B)/P(B).
The "Conditional Probability from a Table" is a top-tier SAT skill. Questions will start with "Of the students who passed the test..." which tells the student to ignore the rest of the table and only look at the "Passed" row.
It teaches students how to update their expectations based on new data and provides a formal test for independence.
The Problem: 60% of students at a high school have a driver's license. 70% of those with a license own a car. Only 10% of those without a license own a car.
Task: Create a tree diagram. What is the probability that a randomly selected student owns a car?
Order Matter (A given B versus B given A)
Independent vs. Disjoint
Support: Use "The Finger Method." On a two-way table, have students literally cover up all rows/columns that do not match the "Given" condition. What's left is their new world.
Extension: Discuss the "Monty Hall Problem" as a way to show how conditional probability can be incredibly counter-intuitive, even for experts.
Teacher assigns examples from the textbook and other resources.
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