Introduction
Experimental Probability is an important Grade 7 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 experimental probability.
What Is Experimental Probability?
Experimental Probability 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 Experimental Probability
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 six-sided die was rolled \(120\) times. The results are shown below. What is the experimental probability of rolling a \(5\)?
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency | 18 | 22 | 19 | 21 | 25 | 15 |
- A. \(\frac{25}{120}\)
- B. \(\frac{7}{24}\)
- C. \(\frac{1}{6}\)
- D. \(\frac{15}{120}\)
Why it works: The face \(5\) appeared \(25\) times out of \(120\) total rolls. Experimental probability \(= \frac{25}{120}\). Note: this is slightly higher than the theoretical probability of \(\frac{1}{6}\).
Answer: \(\frac{25}{120}\)
Visual Model 2
Question: A bag contains marbles of three colors. Maria draws a marble, records the color, and replaces it. After \(300\) draws, the results are: If Maria draws one more marble, which color is she most likely to draw based on experimental probability?
| Color | Red | Blue | Green |
|---|---|---|---|
| Count | 105 | 95 | 100 |
- A. All equally likely
- B. Blue
- C. Green
- D. Red
Why it works: Red has the highest experimental probability: \(\frac{105}{300}=0.35\). From observed patterns, Red appeared most frequently, so we predict it is most likely on the next draw.
Answer: Red
Worked Examples
Example 1
Question: A survey of \(150\) students asked which sport they play. The results: Based on this data, what is the experimental probability that a randomly selected student plays basketball?
| Sport | Soccer | Basketball | Tennis |
|---|---|---|---|
| Students | 48 | 57 | 45 |
- A. \(\frac{57}{105}\)
- B. \(\frac{48}{150}\)
- C. \(\frac{57}{150}\)
- D. \(\frac{45}{150}\)
- Basketball was chosen by \(57\) out of \(150\) students.
- Experimental probability \(= \frac{57}{150}\).
Answer: \(\frac{57}{150}\)
Example 2
Question: A frequency table shows results from drawing cards with replacement \(500\) times: Which suit has the lowest experimental probability?
| Card Type | Hearts | Diamonds | Clubs | Spades |
|---|---|---|---|---|
| Frequency | 140 | 125 | 128 | 107 |
- A. Hearts
- B. Diamonds
- C. Clubs
- D. Spades
- Compare relative frequencies: Hearts \(\frac{140}{500}=0.28\), Diamonds \(\frac{125}{500}=0.25\), Clubs \(\frac{128}{500}=0.256\), Spades \(\frac{107}{500}=0.214\).
- Spades has the lowest.
Answer: Spades
Example 3
Question: A researcher flipped three coins \(160\) times and recorded how many came up heads each time: What is the experimental probability of getting exactly 2 heads?
| Heads Count | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Frequency | 22 | 56 | 62 | 20 |
- A. \(\frac{2}{3}\)
- B. \(\frac{62}{160}\)
- C. \(0.31\)
- D. \(0.39\)
- Getting exactly 2 heads occurred \(62\) times in \(160\) trials.
- Experimental probability \(= \frac{62}{160} = 0.3875 \approx 0.39\).
Answer: \(\frac{62}{160}\)
Real-World Word Problems
Problem 1
Question: A basketball player attempted \(75\) free throws and made \(54\) of them. What is the experimental probability that the player makes the next free throw?
- A. \(0.54\)
- B. \(0.60\)
- C. \(0.67\)
- D. \(0.72\)
Why it works: Experimental probability \(=\frac{54}{75}=0.72\). This relative frequency represents the player's observed success rate and predicts future performance.
Answer: \(0.72\)
Problem 2
Question: Two students tossed a coin. Student A tossed it \(50\) times and got heads \(24\) times. Student B tossed it \(500\) times and got heads \(256\) times. Which experimental probability is closer to the theoretical probability of \(0.5\)?
- A. Student B (\(0.512\))
- B. Cannot determine
- C. Both are equally close
- D. Student A (\(0.48\))
Why it works: Student A: \(\frac{24}{50}=0.48\), difference \(0.02\) from \(0.5\). Student B: \(\frac{256}{500}=0.512\), difference \(0.012\) from \(0.5\). This illustrates the law of large numbers---larger sample sizes yield results closer to theoretical probability.
Answer: Student B (\(0.512\))
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 coin was flipped \(80\) times and came up heads \(36\) times. What is the experimental probability of getting heads?
- A. \(0.36\)
- B. \(0.45\)
- C. \(0.50\)
- D. \(0.56\)
Question 2
A spinner was spun \(200\) times with four equal sections labeled A, B, C, and D. Section A appeared \(58\) times. Which best describes the relationship between the experimental and theoretical probabilities for landing on A?
- A. Both are exactly \(0.25\).
- B. Experimental is \(0.58\); theoretical is \(0.20\).
- C. Experimental is \(0.25\); theoretical is \(0.29\).
- D. Experimental is \(0.29\); theoretical is \(0.25\).
Question 3
A factory tests light bulbs for quality. Out of \(1000\) bulbs tested, \(980\) passed inspection. Based on this experimental data, how many bulbs out of \(5000\) would be expected to pass?
- A. \(980\)
- B. \(3900\)
- C. \(4800\)
- D. \(4900\)
Question 4
A dart was thrown at a target \(400\) times. It hit the bullseye \(92\) times. What is the experimental probability of hitting the bullseye?
- A. \(0.20\)
- B. \(0.23\)
- C. \(0.25\)
- D. \(0.30\)
Question 5
A student rolled a number cube and recorded the results in a bar graph. Out of \(240\) rolls, the number \(6\) appeared in \(38\) rolls. What is the experimental probability of rolling a \(6\)?
- A. \(\frac{1}{6}\)
- B. \(\frac{38}{240}\)
- C. \(0.19\)
- D. \(0.60\)
Question 6
A game involves spinning a spinner. The results of \(600\) spins are shown: If the spinner is spun 1 more time, which outcome has the highest experimental probability of occurring?
| Outcome | Green | Yellow | Purple |
|---|---|---|---|
| Times | 240 | 200 | 160 |
- A. Green
- B. Yellow
- C. Purple
- D. All are equally likely
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(0.45\)
Experimental probability \(=\frac{\text{observed outcomes}}{\text{total trials}}=\frac{36}{80}=0.45\). This is close to the theoretical probability of \(0.5\), showing how observed results approximate expected outcomes.
Question 2
Answer: Experimental: \(\frac{58}{200}=0.29\); Theoretical: \(\frac{1}{4}=0.25\).
Experimental probability (\(0.29\)) is based on observed data and differs from theoretical probability (\(0.25\)) because of random variation. Both values are relative frequencies—ratios of favorable outcomes to total trials.
Question 3
Answer: \(4900\)
Experimental probability of passing \(=\frac{980}{1000}=0.98\). We use this rate to predict outcomes in a larger sample: \(0.98 \times 5000 = 4900\) expected passing bulbs.
Question 4
Answer: \(0.23\)
Experimental probability \(=\frac{92}{400}=0.23\). Distractors represent nearby decimal values that students might compute incorrectly.
Question 5
Answer: \(\frac{38}{240}\)
Experimental probability = \(\frac{\text{observed favorable outcomes}}{\text{total trials}} = \frac{38}{240} \approx 0.158\). This is the relative frequency from the observed data.
Question 6
Answer: Green
Green: \(\frac{240}{600}=0.40\); Yellow: \(\frac{200}{600}\approx0.33\); Purple: \(\frac{160}{600}\approx0.27\). Green has the highest probability.
Connection to Standards
This lesson supports Grade 7 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
Experimental Probability 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.
