# Theoretical Probability Formula

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Probability is the study of the chances of an event occurring or not occurring based on the total number of outcomes possible in a given situation. There are two types of probabilities known as the Theoretical probability and the Empirical probability. Theoretical probability of a certain event is the number of ways in which the event can occur when compared to the total number of outcomes for that event. Theoretical probability arises from a sample space consisting of outcomes which are equally likely to occur.

Example 1: Find the probability of getting a ‘2’ on a rolling fair die.
When a fair die is rolled, there are ‘6’ total number of outcomes possible.
They are: {1, 2, 3, 4, 5, 6}. Hence the sample space for rolling a fair die is ‘6’ equally likely outcomes.
Theoretical probability formula, P(E) = (number of outcomes of the event)/ (Total number of possible outcomes)
Getting a ‘2’ on the fair die has a chance of 1 out of 6 possible outcomes
Therefore, P(E) = 1/6

Example 2: Find the probability of a rolling a fair die and getting an even number.
When a fair die is rolled, there are ‘6’ total number of outcomes possible.
They are: {1, 2, 3, 4, 5, 6}. Hence the sample space for rolling a fair die is ‘6’ equally likely outcomes.
Theoretical probability formula, P(E) = (number of outcomes of the event)/ (Total number of possible outcomes)
Possible outcomes of getting an even number = {2, 4, 6} = 3 outcomes out of 6 total outcomes.
Therefore, P(E) = 3/6 = 1/2