Empirical Probability

Empirical probability is based on observations obtained from probability experiments. It is the ratio of the number of favorable outcomes to the total number of possible outcomes in an experiment. Empirical probability is also known as experimental probability because it is based on actual observations or experiments.

Calculating Empirical Probability

To calculate empirical probability, use the following formula:

Empirical Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes

For example, if you roll a fair six-sided die and you want to find the empirical probability of rolling a 3, you would count the number of times you roll a 3 and divide it by the total number of rolls.

Study Guide

Here are some key points to remember about empirical probability:

Empirical probability is based on actual observations or experiments.
It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Empirical probability can change as more observations are made in an experiment.
It is often used in real-world situations where theoretical probabilities are difficult to calculate.

Practice calculating empirical probability with different experiments and keep track of your observations to better understand this concept.

Remember to always verify your results with a large number of trials to ensure the empirical probability is a good estimate of the true probability.

◂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.

Empirical Probability

Calculating Empirical Probability

Study Guide

[Empirical Probability] Related Worksheets and Study Guides:

◂Math Worksheets and Study Guides Fourth Grade. Probability

The resources above cover the following skills: