Introduction
Probability of Simple and Compound Events is an important Grade 8 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with probability of simple and compound events.
What Is Probability of Simple and Compound Events?
Probability of Simple and Compound Events means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Probability of Simple and Compound Events
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: A spinner has 10 equal sections: 3 red, 4 blue, and 3 yellow. What is the probability of landing on red OR blue?
- A. \(\frac{4}{10}\)
- B. \(\frac{12}{10}\)
- C. \(\frac{7}{10}\)
- D. \(\frac{3}{10}\)
Why it works: \(P(\text{red or blue}) = P(\text{red}) + P(\text{blue}) = \frac{3}{10} + \frac{4}{10} = \frac{7}{10}\).
Answer: \(\frac{7}{10}\)
Visual Model 2
Question: The spinner above is divided into 4 equal sections labeled A, B, C, and D. What is the probability of landing on section A?
- A. \(\frac{1}{4}\)
- B. \(\frac{1}{8}\)
- C. \(\frac{3}{4}\)
- D. \(\frac{1}{2}\)
Why it works: Each section is equal, so each has probability \(\frac{1}{4}\).
Answer: \(\frac{1}{4}\)
Worked Examples
Example 1
Question: A tree diagram shows all possible outcomes when a coin is flipped twice. According to the diagram, how many total outcomes are there?
- A. 2
- B. 6
- C. 4
- D. 3
- The tree diagram shows 4 final branches, one for each outcome: HH, HT, TH, TT.
Answer: 4
Example 2
Question: The table above shows all possible outcomes when selecting a color and a number. How many total outcomes are there?
| 1 | 2 | 3 | |
|---|---|---|---|
| Red | R1 | R2 | R3 |
| Blue | B1 | B2 | B3 |
- A. 5
- B. 6
- C. 8
- D. 9
- The table shows \(2 \times 3 = 6\) outcomes total.
Answer: 6
Example 3
Question: A spinner has 5 equal sections numbered 1--5. Two sections (1 and 2) are shaded. If you spin once, what is the probability of landing on a shaded section?
- A. \(\frac{1}{5}\)
- B. \(\frac{2}{5}\)
- C. \(\frac{3}{5}\)
- D. \(\frac{4}{5}\)
- Two of the five sections are shaded, so \(P(\text{shaded}) = \frac{2}{5}\).
Answer: \(\frac{2}{5}\)
Real-World Word Problems
Problem 1
Question: A spinner is divided into 8 equal sections. If a student spins it once, what is the probability of landing on a specific section? \NumberedSpinner{8}
- A. \(\frac{8}{1}\)
- B. \(\frac{1}{8}\)
- C. \(\frac{1}{2}\)
- D. \(\frac{1}{4}\)
Why it works: Each of the 8 equal sections has probability \(\frac{1}{8}\).
Answer: \(\frac{1}{8}\)
Problem 2
Question: A bag contains 7 red marbles and 3 blue marbles. If two marbles are drawn without replacement, what is the probability that the first is red AND the second is blue?
- A. \(\frac{3}{10}\)
- B. \(\frac{7}{30}\)
- C. \(\frac{21}{100}\)
- D. \(\frac{7}{90}\)
Why it works: \(P(\text{red first}) = \frac{7}{10}\); \(P(\text{blue second | red first}) = \frac{3}{9}\). Product: \(\frac{7}{10} \times \frac{3}{9} = \frac{21}{90} = \frac{7}{30}\).
Answer: \(\frac{7}{30}\)
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
A fair coin is flipped and a standard six-sided die is rolled. What is the probability of getting heads AND a \(4\)?
- A. \(\frac{1}{12}\)
- B. \(\frac{1}{6}\)
- C. \(\frac{1}{8}\)
- D. \(\frac{2}{3}\)
Question 2
A die shows 6 faces numbered 1 through 6. What is the probability of rolling an even number?
- A. \(\frac{1}{6}\)
- B. \(\frac{1}{2}\)
- C. \(\frac{2}{3}\)
- D. \(\frac{1}{3}\)
Question 3
The probability of rain tomorrow is \(\frac{2}{5}\). What is the probability that it will NOT rain?
- A. \(\frac{3}{5}\)
- B. \(\frac{5}{2}\)
- C. \(\frac{1}{5}\)
- D. \(\frac{2}{5}\)
Question 4
A spinner has 5 equal sections labeled 1, 2, 3, 4, 5. You spin it twice. What is the probability of spinning a 3 on the first spin AND a 2 on the second spin? \NumberedSpinner{5}
- A. \(\frac{1}{25}\)
- B. \(\frac{1}{5}\)
- C. \(\frac{2}{25}\)
- D. \(\frac{2}{5}\)
Question 5
A card is drawn from a standard deck. What is the probability that it is either a 5 or a 9?
- A. \(\frac{5}{52}\)
- B. \(\frac{8}{52}\)
- C. \(\frac{4}{52}\)
- D. \(\frac{9}{52}\)
Question 6
Two fair coins are tossed. How many total outcomes are in the sample space?
- A. 2
- B. 4
- C. 8
- D. 3
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(\frac{1}{12}\)
Independent events: \(P(H\text{ and }4)=P(H)\times P(4)=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}\).
Question 2
Answer: \(\frac{1}{2}\)
Even numbers on a die: 2, 4, 6. That's 3 out of 6 outcomes, so \(P(\text{even}) = \frac{3}{6} = \frac{1}{2}\).
Question 3
Answer: \(\frac{3}{5}\)
\(P(\text{not rain}) = 1 - P(\text{rain}) = 1 - \frac{2}{5} = \frac{3}{5}\).
Question 4
Answer: \(\frac{1}{25}\)
\(P(3 \text{ then } 2) = \frac{1}{5} \times \frac{1}{5} = \frac{1}{25}\).
Question 5
Answer: \(\frac{8}{52}\)
These are mutually exclusive. \(P(5 \text{ or } 9) = P(5) + P(9) = \frac{4}{52} + \frac{4}{52} = \frac{8}{52}\).
Question 6
Answer: 4
Sample space: HH, HT, TH, TT. There are 4 total outcomes.
Connection to Standards
This lesson supports Grade 8 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Probability of Simple and Compound Events becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
