# Theoretical and Empirical Probabilities Worksheets

What is the Difference Between Theoretical and Empirical Probabilities? Theoretical probability is the core idea behind probability. When using theoretical probability to predict the occurrence of an event, we do not need to conduct an experiment. In theoretical probability, we should have an idea about the situation and an understanding of the occurrence of an event. Theocratical probability is defined as the ratio of the number of favorable outcomes to the number of possible outcomes. Probability of Even P(E) = Number of favorable outcomes/ Number of Possible outcomes. For instance, if we have to find out the probability of rolling a 5 on a fair die. We do not need to actually roll a die to know the probability. We already know that there are 6 possible outcomes when we roll a die. There are 1, 2, 3, 4, 5, and 6. Hence, using the formula for the theoretical probability: P(E) = Number of favorable outcomes/ Number of Possible outcomes P(E) = 1/6. Therefore, the probability of rolling a 5 on a fair die is 1/6. Empirical probability is found by conducting experiments and through observations. The likelihood that the event will happen is based on the results obtained from the collected data. The mathematical formula for finding empirical probability is written as: Empirical Probability = Number of times an event can take place/ total number of trials. For instance, a fair die is rolled 120 times, and you to find out the number of times 5 turned up. We know that each number on the die has an equal probability of 1/6. Therefore, the probability of 5 turning up is also 1/6. So, we will calculate 120 x 1/6= 20. The probability of 5 is 20 out of 120.

• ### Basic Lesson

Guides students solving equations that involve an theoretical and empirical probabilities. Demonstrates answer checking. At a school fair, the spinner represented in the accompanying diagram is spun twice. What is the probability that it will land in section G the first time and then in section B the second time?

• ### Intermediate Lesson

Demonstrates how to solve more difficult problems. The accompanying figure is a square. The interior sections are formed using congruent squares. If this figure is used as a dart board, what is the probability that the dart will hit the shaded blue region?

• ### Independent Practice 1

A really great activity for allowing students to understand the concept of theoretical and empirical probabilities. A bag of cookies contains 10 chocolate chip cookies, 8 peanut butter cookies, and 2 oatmeal cookie. Brandon selects 2 cookies at random. Find the probability 2 chocolate chip cookies.

• ### Independent Practice 2

Students find the theoretical and empirical probabilities in assorted problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with problems to achieve the concepts of theoretical and empirical probabilities.

• ### Skill Quiz

This tests the students ability to evaluate theoretical and empirical probabilities.