Lesson 6: 5.6: The Multiplication Rule for Independent Events

If a coin is flipped 10 times, why is the probability of 10 heads so much smaller than the probability of 1 head?

What is the "test" for independence using the multiplication rule?

Multiplication Rule for Independent Events

Sampling with Replacement

Sampling without Replacement

HSS-CP.A.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities.

If the SAT states that two events are independent, they expect you to immediately know you can multiply their probabilities together to find the "both" scenario.

This section teaches students that when events don't affect each other (like dice rolls), the math becomes significantly simpler.

The Problem: A surgical procedure has an 85% success rate. If the procedure is performed on three independent patients, what is the probability that all three surgeries are successful?

Assuming Independence: Students often multiply probabilities for events that are clearly dependent (like drawing two cards from a deck without replacement).

Use the "Replacement vs. No Replacement" demonstration with a bag of colored candies to show how the "denominator" changes (or doesn't).

Teacher assigns examples from the textbook and other resources.

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