A focused Grade 7 learning session for Experimental Probability using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving experimental probability.
Experimental Probability is part of Grade 7 Probability. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of experimental probability using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Experimental Probability, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving experimental probability.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A coin was flipped \(80\) times and came up heads \(36\) times. What is the experimental probability of getting heads?
Answer B: \(0.45\)
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.
A six-sided die was rolled \(120\) times. The results are shown below. What is the experimental probability of rolling a \(5\)?
Answer A: \(\frac{25}{120}\)
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 \(\frac{1}{6}\).
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?
Answer D: Experimental is \(0.29\); theoretical is \(0.25\).
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.
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?
Answer D: \(0.72\)
Experimental probability \(=\frac{54}{75}=0.72\). This relative frequency represents the player's observed success rate and predicts future performance.
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?
Answer D: Red
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.
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?
Answer C: \(\frac{57}{150}\)
Basketball was chosen by \(57\) out of \(150\) students. Experimental probability \(= \frac{57}{150}\).
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 \(0.5\)?
Answer A: Student B (\(0.512\))
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.
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?
Answer D: \(4900\)
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.
A dart was thrown at a target \(400\) times. It hit the bullseye \(92\) times. What is the experimental probability of hitting the bullseye?
Answer B: \(0.23\)
Experimental probability \(=\frac{92}{400}=0.23\). Distractors represent nearby decimal values that students might compute incorrectly.
A frequency table shows results from drawing cards with replacement \(500\) times: Which suit has the lowest experimental probability?
Answer 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.
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 \(6\)?
Answer B: \(\frac{38}{240}\)
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.
