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Probability Models and Experimental Probability

Students build probability models and compare theoretical probability with long-run experimental results.

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Beginner 15–20 minutes Probability & Statistics
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At a Glance

Probability Models and Experimental Probability
Binder SectionProbability & Statistics
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
Essential Question

How can simulation estimate probabilities that are difficult to calculate directly?

Build Understanding

Probability measures likelihood from 0 to 1. In an equally likely sample space, P(event) = favorable outcomes divided by total outcomes. The probabilities of all outcomes in a valid model sum to 1.

Theoretical probability comes from a model; experimental probability comes from observed trials. With many fair, independent trials, experimental results tend to approach the theoretical probability.

Visual Model
4Thousands 3Hundreds 2Tens 7Ones

4,327 = 4,000 + 300 + 20 + 7

Goals

Learning Targets

  • 0 means impossible; 1 means certain.
  • List the sample space carefully.
  • P(not A) = 1 - P(A).
  • Experimental probability = successes divided by trials.
  • More trials usually stabilize relative frequency.
Click each word

Interactive Vocabulary

Reveal one step at a time

Worked Examples

Example 1

Simulate three coin flips with random digits 0–4 as heads and 5–9 as tails.

1

Record whether at least two heads occur.

Example 2

Worked Example 2

1

Compare simulated frequency with exact probability 4/8=1/2.

Ask and explain

Common Questions

Must all outcomes be equally likely? No; only use simple counting when they are.
Does a probability of one-half guarantee half the next ten trials? No.
Can experimental probability differ from theory? Yes, especially with few trials.
Notice and correct

Common Misconceptions

Using a simulation that does not preserve probabilities

Match each outcome to proportional random-number ranges.

Drawing a conclusion from too few trials

Increase trials and report variability.

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Probability Models and Simulation lesson and examples

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1
Quick Start

Warm-Up

Warm-up 1

Directions: Solve the problem. Show your thinking, then enter only your final answer.

A fair event has probability 0.30. Assign random digits 0–9.

Organize 0.30 by place valueUse the picture to organize what you know before you solve.

Choose how you want to work or answer.

2
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Guided Practice

3
You Do

Independent Practice

Independent 1

Directions: Solve independently. Show your work, check it, then enter only your final answer.

A fair event has probability 0.30. Assign random digits 0–9.

Organize 0.30 by place valueUse the picture to organize what you know before you solve.

Choose how you want to work or answer.

Independent 2

Directions: Solve independently. Show your work, check it, then enter only your final answer.

Create and solve a second example with different values.

Picture the possible outcomesUse the picture to organize what you know before you solve.
ABCD

Choose how you want to work or answer.

4
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Challenge & Real-World Practice

🧩 Challenge

Design a valid simulation for a real multistage situation, run enough trials, and compare the estimate with an exact or reasoned benchmark.

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Success Criteria

Before you begin, I can…

  • I can identify the important information.
  • I can use accurate notation, labels, and units.
  • I can justify and verify my conclusion.
1
Question 1

What should happen before calculating?

2
Question 2

Which response gives the strongest evidence?

3
Question 3

What is an effective accuracy check?

4
Question 4

Why are units or labels important?

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Question 5

What should a student do after finding an error?

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