Grade 7 · Statistics & Probability · MAT-07-SP-005
Build Probability Models
Represent and solve build probability models problems using precise mathematical notation, models, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve build probability models problems using precise mathematical notation, models, and reasoning.
- Explain why a method for build probability models works, interpret the result in context, and verify it independently.
Prerequisite check
Make sure the foundation is ready.
The new lesson depends on this prerequisite as active knowledge.
Learn
Build the idea from meaning, not memorization.
Mathematical meaning
Build Probability Models describes data or chance while accounting for variability. Calculations must be interpreted in the context of data collection or a probability model.
Represent the relationship
The Math Box uses probability simulator to expose the structure. Change one input, predict the result, then connect the visual change to an equation, table, graph, number line, or geometric model.
Calculate, interpret, and verify
Verify calculations from the raw values, then decide whether the sample, display, center, spread, or probability model actually supports the claim.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Probability Lab
- Model one example of build probability models in the Math Box.
- Change one input, predict the effect, and test the prediction.
- State the relationship or invariant that explains what stayed mathematically consistent.
Worked examples
Twenty different ways to see the concept work.
A model has 1 favorable equally likely outcomes out of 3. Find P(event).
P = 1/3 = 0.333For equally likely outcomes, probability is favorable divided by total.
A model has 2 favorable equally likely outcomes out of 5. Find P(event).
P = 2/5 = 0.4For equally likely outcomes, probability is favorable divided by total.
A model has 3 favorable equally likely outcomes out of 7. Find P(event).
P = 3/7 = 0.429For equally likely outcomes, probability is favorable divided by total.
A model has 4 favorable equally likely outcomes out of 9. Find P(event).
P = 4/9 = 0.444For equally likely outcomes, probability is favorable divided by total.
A model has 5 favorable equally likely outcomes out of 11. Find P(event).
P = 5/11 = 0.455For equally likely outcomes, probability is favorable divided by total.
A model has 1 favorable equally likely outcomes out of 8. Find P(event).
P = 1/8 = 0.125For equally likely outcomes, probability is favorable divided by total.
A model has 2 favorable equally likely outcomes out of 4. Find P(event).
P = 2/4 = 0.5For equally likely outcomes, probability is favorable divided by total.
A model has 3 favorable equally likely outcomes out of 6. Find P(event).
P = 3/6 = 0.5For equally likely outcomes, probability is favorable divided by total.
A model has 4 favorable equally likely outcomes out of 8. Find P(event).
P = 4/8 = 0.5For equally likely outcomes, probability is favorable divided by total.
A model has 5 favorable equally likely outcomes out of 10. Find P(event).
P = 5/10 = 0.5For equally likely outcomes, probability is favorable divided by total.
A model has 1 favorable equally likely outcomes out of 7. Find P(event).
P = 1/7 = 0.143For equally likely outcomes, probability is favorable divided by total.
A model has 2 favorable equally likely outcomes out of 9. Find P(event).
P = 2/9 = 0.222For equally likely outcomes, probability is favorable divided by total.
A model has 3 favorable equally likely outcomes out of 5. Find P(event).
P = 3/5 = 0.6For equally likely outcomes, probability is favorable divided by total.
A model has 4 favorable equally likely outcomes out of 7. Find P(event).
P = 4/7 = 0.571For equally likely outcomes, probability is favorable divided by total.
A model has 5 favorable equally likely outcomes out of 9. Find P(event).
P = 5/9 = 0.556For equally likely outcomes, probability is favorable divided by total.
A model has 1 favorable equally likely outcomes out of 6. Find P(event).
P = 1/6 = 0.167For equally likely outcomes, probability is favorable divided by total.
A model has 2 favorable equally likely outcomes out of 8. Find P(event).
P = 2/8 = 0.25For equally likely outcomes, probability is favorable divided by total.
A model has 3 favorable equally likely outcomes out of 10. Find P(event).
P = 3/10 = 0.3For equally likely outcomes, probability is favorable divided by total.
A model has 4 favorable equally likely outcomes out of 6. Find P(event).
P = 4/6 = 0.667For equally likely outcomes, probability is favorable divided by total.
A model has 5 favorable equally likely outcomes out of 8. Find P(event).
P = 5/8 = 0.625For equally likely outcomes, probability is favorable divided by total.
Practice
Guided practice with hints
01A model has 1 favorable equally likely outcomes out of 5. Find P(event).
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: P = 1/5 = 0.2
02A model has 2 favorable equally likely outcomes out of 7. Find P(event).
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: P = 2/7 = 0.286
03A model has 3 favorable equally likely outcomes out of 9. Find P(event).
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: P = 3/9 = 0.333
04A model has 4 favorable equally likely outcomes out of 11. Find P(event).
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: P = 4/11 = 0.364
05A model has 5 favorable equally likely outcomes out of 7. Find P(event).
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: P = 5/7 = 0.714
06A model has 1 favorable equally likely outcomes out of 4. Find P(event).
Hint: Represent the relationship first, keep units visible, and identify a second verification method.
Answer: P = 1/4 = 0.25
Practice
Independent practice
01A model has 2 favorable equally likely outcomes out of 6. Find P(event).
Answer: P = 2/6 = 0.333
02A model has 3 favorable equally likely outcomes out of 8. Find P(event).
Answer: P = 3/8 = 0.375
03A model has 4 favorable equally likely outcomes out of 10. Find P(event).
Answer: P = 4/10 = 0.4
04A model has 5 favorable equally likely outcomes out of 12. Find P(event).
Answer: P = 5/12 = 0.417
05A model has 1 favorable equally likely outcomes out of 3. Find P(event).
Answer: P = 1/3 = 0.333
06A model has 2 favorable equally likely outcomes out of 5. Find P(event).
Answer: P = 2/5 = 0.4
07A model has 3 favorable equally likely outcomes out of 7. Find P(event).
Answer: P = 3/7 = 0.429
08A model has 4 favorable equally likely outcomes out of 9. Find P(event).
Answer: P = 4/9 = 0.444
Common mistakes
Learn to catch the error, not just the answer.
Interpret center with spread, shape, and sampling method.
Finite experimental frequencies vary even when a model is correct.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Summarize data, compare groups, evaluate survey claims, and describe uncertainty.
- Build probability models and simulations for repeated random processes.
Challenge problems
A model has 5 favorable equally likely outcomes out of 11. Find P(event).
P = 5/11 = 0.455
A model has 1 favorable equally likely outcomes out of 8. Find P(event).
P = 1/8 = 0.125
A model has 2 favorable equally likely outcomes out of 4. Find P(event).
P = 2/4 = 0.5
A model has 3 favorable equally likely outcomes out of 6. Find P(event).
P = 3/6 = 0.5
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 7 Reasoning Sprint
Solve build probability models problems accurately and justify each result with a valid check.
Practice
Mastery check
01A model has 4 favorable equally likely outcomes out of 8. Find P(event).
Answer: P = 4/8 = 0.5
02A model has 5 favorable equally likely outcomes out of 10. Find P(event).
Answer: P = 5/10 = 0.5
03A model has 1 favorable equally likely outcomes out of 7. Find P(event).
Answer: P = 1/7 = 0.143
04A model has 2 favorable equally likely outcomes out of 9. Find P(event).
Answer: P = 2/9 = 0.222
05A model has 3 favorable equally likely outcomes out of 5. Find P(event).
Answer: P = 3/5 = 0.6
06A model has 4 favorable equally likely outcomes out of 7. Find P(event).
Answer: P = 4/7 = 0.571
07A model has 5 favorable equally likely outcomes out of 9. Find P(event).
Answer: P = 5/9 = 0.556
08A model has 1 favorable equally likely outcomes out of 6. Find P(event).
Answer: P = 1/6 = 0.167
Terminology
Words to know
- distribution
- The pattern of values including center, spread, shape, and unusual features.
- variability
- The degree to which observations differ.
- sample
- A subset of a population used to collect information.
- probability
- A number from 0 to 1 describing likelihood.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Middle-school instructional guidance, mathematical practices, modeling, and coherent progression.Common Core State Standards for Mathematics — Grade 7
Grade-level expectations for ratios, number systems, algebra, geometry, statistics, and probability.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.