Probability is a measure that quantifies the likelihood or chance of an event occurring. In the field of statistics and probability theory, it provides a way to express uncertainty and quantify the likelihood of various outcomes in a given situation. Probability is usually expressed as a number between 0 and 1, where 0 indicates impossibility (the event will not occur), and 1 indicates certainty (the event will occur). For example :
Suppose you have a fair six-sided die. The die has numbers from 1 to 6 on its faces, and each face is equally likely to come up when the die is rolled.
Theoretical Probability:
The probability of rolling a 3 (P(3)) can be calculated as the number of favorable outcomes (rolling a 3) divided by the total number of possible outcomes (numbers 1 through 6). P(3) = ⅙
Empirical Probability:
If you were to roll the die 100 times and count how many times you roll a 3, the empirical probability of rolling a 3 would be the number of times you roll a 3 divided by the total number of rolls. Let’s say you roll a 3 20 times out of 100 rolls, then the empirical probability is 20/100 = ⅕
In the above example:
Theoretical probability is based on the assumption of an idealized, fair die. Empirical probability is based on actual observations from a specific experiment.
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