Theoretical Versus Empirical Probability Worksheets

What is the Difference Between Theoretical and Empirical Probability? Empirical probability is the type of probability 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 Probability = 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 probability of 4 is 30 out of 180. 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 4 on a fair die. We do not need to 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 4 on a fair die is 1/6.