Compound Events Mastery Worksheet
Lesson 8.5 • SP8 Probability & Statistics
Compound Events Mastery
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Core Concept: Independent vs. Dependent Compound Events
With Replacement (Independent): The item is returned. The total outcomes and favorable counts stay the same for the second pick.
Without Replacement (Dependent): The item is NOT returned. Total outcomes decrease by 1, and the count for that item's color also drops if picked.
FOCUS LESSON - PART 1 Without Replacement
Bag A: 5 Purple, 1 Orange, 1 Brown (7 Total)
Two marbles in a row are picked at random. Without putting the first marble back, a second marble is picked at random. Find the probability that the first marble picked is orange and the second marble picked is purple.
Generate a multiplication expression to determine the probability. Simplify to a percentage.
BAG A CONTENTS
P
P
P
P
P
O
B
Total = 7 Marbles
Show your work below (Multiplication Expression → Simplified Fraction → Percentage): P(Orange, then Purple)
FOCUS LESSON - PART 2 With Replacement
Bag A: 5 Purple, 1 Orange, 1 Brown (7 Total)
Two marbles in a row are picked at random from a bag. The first marble is replaced back into the bag of marbles, then a second marble is picked at random. Find the probability that the first marble picked is brown and the second marble picked is purple.
Generate a multiplication expression to determine the probability. Simplify to a percentage.
BAG A CONTENTS
P
P
P
P
P
O
B
Total = 7 Marbles
Show your work below (Multiplication Expression → Simplified Fraction → Percentage): P(Brown, then Purple)
Lesson 8.5 • Compound Probability Page 1 of 5
Lesson 8.5 • SP8
Sample Spaces & Tree Diagrams
Total Outcomes: \(6 \times 6 = 36\) Possible Pairs
TREE DIAGRAM: TWO ROLLS OF A 6-SIDED NUMBER CUBE Roll 1 (Top Nodes 1–6) → Roll 2 (Leaves 1–6)
FIRST ROLL (OUTCOMES 1 TO 6) 1 1 2 3 4 5 6 2 1 2 3 4 5 6 3 1 2 3 4 5 6 4 1 2 3 4 5 6 5 1 2 3 4 5 6 6 1 2 3 4 5 6 Second Roll Outcomes (1 through 6 for each First Roll)
FOCUS LESSON - PART 3a Event: Sum of Two Rolls
Scenario: A teacher has a number cube with faces numbered 1 through 6. He will roll the number cube two times. Each time the teacher rolls the number cube, he will record the number shown on the top face. Then he will find the sum of the two numbers he records.
What is the probability that the sum of the numbers he records will be 8? Write your answer as a fraction in simplest form.
List all favorable pairs \((r_1, r_2)\) that add to 8:
Probability Calculation:
Favorable: _____
Total: 36
P(Sum = 8) = ______
FOCUS LESSON - PART 3b Event: Product of Two Rolls
Scenario: Using the same tree diagram of 36 outcomes, the teacher rolls the number cube two times and records the two numbers. This time, he calculates the product (multiplication) of the two numbers.
What is the probability that the product of the numbers he records will be greater than 10? Write your answer as a simplified fraction and percentage.
Show organized work (list or count favorable products > 10):
Final Probability:
Favorable: _____ / 36
Fraction: _______
Percent: ≈ ______%
Lesson 8.5 • Tree Diagrams & Sample Spaces Page 2 of 5
Guided Practice • SP8
Tree Diagram Mastery & Analysis
Total Outcomes: \(6 \times 6 = 36\) Possible Pairs
SAMPLE SPACE TREE DIAGRAM: TWO ROLLS OF A NUMBER CUBE Use the branches below to count outcomes
FIRST ROLL (OUTCOMES 1 TO 6) 1 1 2 3 4 5 6 2 1 2 3 4 5 6 3 1 2 3 4 5 6 4 1 2 3 4 5 6 5 1 2 3 4 5 6 6 1 2 3 4 5 6 Second Roll Outcomes (1 through 6 for each First Roll)
PRACTICE - PART 4a Event: Sum is a Multiple of 4
Scenario: A teacher rolls a 6-sided number cube two times and records the top face for each roll. He calculates the sum of the two numbers.
What is the probability that the sum of the numbers he records will be a multiple of 4 ? Write your answer as a simplified fraction and percentage.
List all favorable pairs \((r_1, r_2)\) for Sum = 4, 8, or 12:
Probability Calculation:
Favorable: _____ / 36
Fraction: _______
Percent: ______%
PRACTICE - PART 4b Event: Product is an Odd Number
Scenario: Using the tree diagram, the teacher rolls the number cube two times. This time, he calculates the product (multiplication) of the two numbers.
What is the probability that the product of the numbers will be an odd number? Write your answer as a simplified fraction and percentage.
Show organized work (list odd pairs from {1, 3, 5}):
Final Probability:
Favorable: _____ / 36
Fraction: _______
Percent: ______%
Lesson 8.5 • Tree Diagrams & Sample Spaces Page 3 of 5
Guided Practice
Marble Bag Compound Events
Carefully note: replacement vs. non-replacement
Bag A Reference 7 Total
5 Purple, 1 Orange/Yellow, 1 Brown
Bag A Marbles
P
P
P
P
P
O
B
Bag B Reference 6 Total
3 Green, 2 Red, 1 Brown
Bag B Marbles
G
G
G
R
R
B
GP1 WITHOUT REPLACEMENT
From Bag A, two marbles in a row are picked at random. Without putting the first marble back, a second marble is picked.
Find \(P(\text{Purple, then Yellow/Orange})\).
Write multiplication expression & percentage:
Expr: ___________ %: _______%
GP2 WITH REPLACEMENT
From Bag B, two marbles in a row are picked at random. The first marble is replaced back, then a second marble is picked.
Find \(P(\text{Red, then Green})\).
Write multiplication expression & percentage:
Expr: ___________ %: _______%
GP3 WITH REPLACEMENT
From Bag A, two marbles in a row are picked. The first marble is replaced back into the bag, then a second marble is picked at random.
Find \(P(\text{Purple, then Purple})\).
Write multiplication expression & percentage:
Expr: ___________ %: _______%
GP4 WITHOUT REPLACEMENT
From Bag B, two marbles in a row are picked. Without replacement, a second marble is picked at random.
Find \(P(\text{Brown, then Green})\).
Write multiplication expression & percentage:
Expr: ___________ %: _______%
Key Checkpoint: When picking without replacement, remember that the second fraction's denominator must be reduced by 1 because total marbles went from \(n\) to \(n-1\)!
Lesson 8.5 • Marble Compound Probability Page 4 of 5
Guided Practice
Multi-Stage Independent Events
Coins, Dice & Number Cards
Multiplication Rule for Independent Events: \(P(A \text{ and } B) = P(A) \times P(B)\) | Events do NOT affect one another
GP6 Coin & Standard 6-Sided Die
A coin is flipped and then a standard 6-sided die is rolled. What is the probability of landing on tails and then rolling an even number?
T
⚁
Show work: \(P(\text{Tails}) \times P(\text{Even})\)
Answer P = ______
GP7 Complementary Event (Not a 3)
A coin is flipped and then a die is rolled. What is the probability of landing on tails and then rolling a number that is not a 3?
T
≠3
Show work: \(P(\text{Tails}) \times P(\text{Not 3})\)
Answer P = ______
GP8 Number Cards & Coin Flip
A card is picked from the set shown below and then a coin is flipped. What is the probability of picking a card that is not even (odd) and then landing on heads?
3 4 5 6 7 8
H
Show work: Identify odd cards in {3,4,5,6,7,8} → Multiply by \(P(\text{Heads})\)
Answer P = ______
Self-Check & Reflection:
Explain in one sentence why flipping a coin and rolling a die is considered an independent compound event:
Lesson 8.5 • Independent Events Practice Page 5 of 5
