Theoretical Probability

Theoretical probability is the likelihood of a specific event happening based on all possible outcomes. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Calculating Theoretical Probability

To calculate the theoretical probability of an event, you can use the following formula:

Probability (P) = Number of favorable outcomes / Total number of possible outcomes

Example

Suppose you have a standard six-sided die. To find the theoretical probability of rolling a 3, you would use the formula:

Probability of rolling a 3 = 1 (since there is one favorable outcome - rolling a 3) / 6 (since there are six possible outcomes when rolling a six-sided die)

So, the theoretical probability of rolling a 3 on a standard six-sided die is 1/6.

Study Guide

Understand the concept of theoretical probability and how it relates to the likelihood of an event occurring.
Learn how to calculate theoretical probability using the formula: P = Number of favorable outcomes / Total number of possible outcomes.
Practice calculating theoretical probability with different examples, such as coin flips, dice rolls, and card draws.
Understand the difference between theoretical probability and experimental probability, and when each is used.

Remember, theoretical probability gives us an idea of what should happen, while experimental probability tells us what actually happened through experiments or observations. With practice, you can become comfortable with calculating theoretical probabilities for various scenarios.

◂Math Worksheets and Study Guides Fourth Grade. Probability

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Data Analysis and Probability (NCTM)

Understand and apply basic concepts of probability.

Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible.

Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1.

Connections to the Grade 4 Focal Points (NCTM)

Number and Operations: Building on their work in grade 3, students extend their understanding of place value and ways of representing numbers to 100,000 in various contexts. They use estimation in determining the relative sizes of amounts or distances. Students develop understandings of strategies for multi-digit division by using models that represent division as the inverse of multiplication, as partitioning, or as successive subtraction. By working with decimals, students extend their ability to recognize equivalent fractions. Students' earlier work in grade 3 with models of fractions and multiplication and division facts supports their understanding of techniques for generating equivalent fractions and simplifying fractions.

Theoretical Probability

Calculating Theoretical Probability

Example

Study Guide

[Theoretical Probability] Related Worksheets and Study Guides:

◂Math Worksheets and Study Guides Fourth Grade. Probability

The resources above cover the following skills: