Algebra 2 Honors Lesson

Independent Events and the Multiplication Rule

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10-11BTC Style / Thinking Classrooms12-190 min

Learning Objective

Students will determine whether two events are independent and apply the Multiplication Rule to calculate the probability of two or more independent events occurring together.

Lesson Overview

Students progress from identifying independent events by intuition to applying the Multiplication Rule P(A and B) = P(A)·P(B) in multi-step and conditional contexts, building fluency through collaborative vertical-surface work.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors)
Erasers or paper towels
Standard six-sided dice (2 per group)
Coins (2 per group)
Printed task cards (optional)
Calculators

Scaffolded Task Progression

1Task 1

A fair coin is flipped once and a fair six-sided die is rolled once.

1. Does the result of the coin flip change the probability of any number on the die? Explain.
2. What is

P (Heads)

?
3. What is

P (rolling a 4)

?
4. List the sample space for (coin, die). How many outcomes are there?

2Task 2

Using the coin-and-die experiment from Task 1:

1. Out of 12 equally likely outcomes, how many show (Heads AND a 4)?
2. So

P (Heads AND rolling a 4) =

?
3. Now compute

P (Heads) \times P (rolling a 4)

.
4. What do you notice?

3Task 3

A bag contains 3 red and 7 blue marbles. A marble is drawn, its color is recorded, and it is replaced before a second draw.

1. Are the two draws independent? Explain.
2. Find

P (Red on draw 1 AND Red on draw 2)

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