Learn on PengienVision, Mathematics, Grade 7Chapter 7: Probability

Lesson 4: Use Probability Models

In this Grade 7 lesson from enVision Mathematics Chapter 7, students learn how to develop and use probability models by identifying sample spaces and calculating theoretical and experimental probabilities of events. They practice listing all possible outcomes, assigning probabilities to each event, and using proportional reasoning to make estimates based on experimental data. The lesson also distinguishes between theoretical probability and experimental probability using real-world scenarios involving marble draws.

Section 1

Constructing Probability Models

Property

An experiment is an activity with an observable result. The set of all possible outcomes is called the sample space. An event is any subset of a sample space. The probability of an event p is a number that always satisfies 0≤p≤10 \le p \le 1. A probability model is a mathematical description of an experiment listing all possible outcomes and their associated probabilities. The sum of the probabilities must equal 1. To construct a model for an event with equally likely outcomes, identify every outcome, determine the total number of outcomes, and express each outcome's probability as a ratio to the total.

Examples

  • A fair coin is tossed. The sample space is {Heads, Tails}. The probability model is P(Heads) = 12\frac{1}{2} and P(Tails) = 12\frac{1}{2}.
  • A spinner has four equal sections colored Red, Green, Blue, and Yellow. The probability of landing on any specific color is 14\frac{1}{4}.

Section 2

Application: Making Predictions with Probability Models

Property

To predict future outcomes using experimental probability:
Expected number of occurrences = P(event)×number of future trialsP(\text{event}) \times \text{number of future trials}, where P(event)P(\text{event}) is the experimental probability from past trials.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Constructing Probability Models

Property

An experiment is an activity with an observable result. The set of all possible outcomes is called the sample space. An event is any subset of a sample space. The probability of an event p is a number that always satisfies 0≤p≤10 \le p \le 1. A probability model is a mathematical description of an experiment listing all possible outcomes and their associated probabilities. The sum of the probabilities must equal 1. To construct a model for an event with equally likely outcomes, identify every outcome, determine the total number of outcomes, and express each outcome's probability as a ratio to the total.

Examples

  • A fair coin is tossed. The sample space is {Heads, Tails}. The probability model is P(Heads) = 12\frac{1}{2} and P(Tails) = 12\frac{1}{2}.
  • A spinner has four equal sections colored Red, Green, Blue, and Yellow. The probability of landing on any specific color is 14\frac{1}{4}.

Section 2

Application: Making Predictions with Probability Models

Property

To predict future outcomes using experimental probability:
Expected number of occurrences = P(event)×number of future trialsP(\text{event}) \times \text{number of future trials}, where P(event)P(\text{event}) is the experimental probability from past trials.

Examples