#### The empirical probability (also known as relative frequency or experimental) of an event is expressed as a ratio of the number of outcomes in which a specified event occurs to the total number of trials in an actual experiment. Theoretical probability is based on thinking through the situation. It is expressed as a ratio of the number of favorable outcomes to the number of possible outcomes. In these worksheets, students will learn about the differences and exceptions between the theoretical and empirical forms. They will learn to identify when a calculated likelihood is theoretical and when it is empirical. They will solve problems to calculate both empirical and theoretical forms of possibility. This set of worksheets contains lessons, step-by-step solutions to sample problems, both simple and more complex problems, reviews, and quizzes. When finished with this set of worksheets, students will be able to calculate and differentiate between empirical and theoretical forms of possibilities.

Typically, probability is the likelihood of the occurrence of an event. We can write it in the forms of decimals and fractions. When probability is represented in decimal form, it ranges for 0 to 1. When an event shows a likelihood of 0, it means that a particular event has zero chances of taking place. However, when an event has a likelihood of 1, it means that a particular event will take place. When the likelihood is closer to 1, then the event is likely to happen, and when the likelihood is closer to 0, then it is less likely that an event would happen. For instance, an event with a likelihood of 0.7 is more likely to happen than an event with a likelihood of 0.1 Empirical probability is the type of prospect that is calculated by doing experiments and conducting observations. The likelihood that the event will happen is based on the results obtained from the collected data. The mathematical formula for calculating empirical probability is written as: Empirical = Number of times an event can take place / total number of trials. For instance, a fair die is rolled 180 times, and you to find out the number of times 4 turned up. We know that each number on the die has an equal probability of 1/6. Therefore, the probability of 4 turning up is also 1/6. So, we will calculate 180 x 1/6= 30. The expectation of 4 is 30 out of 180. These worksheets explain how to determine and differentiate between empirical and theoretical probability. Sample problems are solved and practice problems are provided.