Learn on PengiReveal Math, AcceleratedUnit 10: Probability

Lesson 10-3: Theoretical Probability of Simple Events

In this Grade 7 lesson from Reveal Math, Accelerated (Unit 10: Probability), students learn how to calculate the theoretical probability of simple events using the ratio of favorable outcomes to total possible outcomes. The lesson introduces the uniform probability model and guides students through real-world examples, such as determining the probability of choosing scissors in rock, paper, scissors or selecting a specific shirt color from a closet. Students also practice expressing probability as a fraction, decimal, and percent across a variety of contexts.

Section 1

Counting Favorable Outcomes and Total Trials

Property

An event is a specific outcome or a collection of outcomes. The outcomes that make an event happen are called favorable outcomes. To find the number of favorable outcomes, identify all the possible results that match the event's description and count them.

Examples

Section 2

Defining Theoretical Probability and Sample Space

Property

A sample space is the list of all possible outcomes for a probability experiment. An event is a subset of the sample space.
Theoretical probability is calculated as:

P(event)=number of favorable outcomestotal number of possible outcomesP(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}

A uniform probability model assigns equal probability to all outcomes in the sample space.

Examples

  • When rolling a standard six-sided die, the sample space is {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\}. The probability of the event 'rolling an even number' is P(even)=36=12P(\text{even}) = \frac{3}{6} = \frac{1}{2}.
  • When flipping a coin, the sample space is {heads,tails}\{\text{heads}, \text{tails}\}. This is a uniform model where P(heads)=P(tails)=12P(\text{heads}) = P(\text{tails}) = \frac{1}{2}.
  • In a class of 20 students, if a student is selected at random, the probability that any specific student like Sam is selected is P(Sam)=120P(\text{Sam}) = \frac{1}{20}.

Explanation

Understanding sample spaces and theoretical probability provides the foundation for analyzing more complex situations. By identifying all possible outcomes and counting favorable ones, we can calculate exact probabilities for events. This theoretical approach will be essential when working with compound events involving multiple steps or conditions.

Section 3

Predicting Outcomes using Theoretical Probability

Property

You can use the theoretical probability of an event to predict how many times that event is expected to occur over a certain number of trials.

Expected Outcomes=P(event)×Total Number of Trials\text{Expected Outcomes} = P(\text{event}) \times \text{Total Number of Trials}

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Counting Favorable Outcomes and Total Trials

Property

An event is a specific outcome or a collection of outcomes. The outcomes that make an event happen are called favorable outcomes. To find the number of favorable outcomes, identify all the possible results that match the event's description and count them.

Examples

Section 2

Defining Theoretical Probability and Sample Space

Property

A sample space is the list of all possible outcomes for a probability experiment. An event is a subset of the sample space.
Theoretical probability is calculated as:

P(event)=number of favorable outcomestotal number of possible outcomesP(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}

A uniform probability model assigns equal probability to all outcomes in the sample space.

Examples

  • When rolling a standard six-sided die, the sample space is {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\}. The probability of the event 'rolling an even number' is P(even)=36=12P(\text{even}) = \frac{3}{6} = \frac{1}{2}.
  • When flipping a coin, the sample space is {heads,tails}\{\text{heads}, \text{tails}\}. This is a uniform model where P(heads)=P(tails)=12P(\text{heads}) = P(\text{tails}) = \frac{1}{2}.
  • In a class of 20 students, if a student is selected at random, the probability that any specific student like Sam is selected is P(Sam)=120P(\text{Sam}) = \frac{1}{20}.

Explanation

Understanding sample spaces and theoretical probability provides the foundation for analyzing more complex situations. By identifying all possible outcomes and counting favorable ones, we can calculate exact probabilities for events. This theoretical approach will be essential when working with compound events involving multiple steps or conditions.

Section 3

Predicting Outcomes using Theoretical Probability

Property

You can use the theoretical probability of an event to predict how many times that event is expected to occur over a certain number of trials.

Expected Outcomes=P(event)×Total Number of Trials\text{Expected Outcomes} = P(\text{event}) \times \text{Total Number of Trials}