Emperical Probability
In practice the true possible outcomes/likelihoods are impossible to know, so instead we repeatedly perform the experiment to observe the number of times an outcome happens.
Empirical Probability the observed probability of an outcome.
Given a frequency table, the probability of an event being in a given class is:
\[P(E)=\frac{\text{frequency of the class}}{\text{total frequencies in the table}}=\frac{f}{n}\]
At a recent blood drive at SMWC, there were 50 blood donors, the blood type of each donor was collected in the following table. What is the empirical probability of randomly selecting someone and they have blood type O.
| Blood Type | Frequency |
| A | 22 |
| B | 5 |
| AB | 2 |
| O | 21 |
| Total | 50 |
\[P(\text{Blood Type O})=\frac{\text{number of donors of blood type O}}{\text{number of total donors}}=\frac{21}{50}=0.42\]
Law of Large Numbers given enough repeated attempts at the experiment the empirical experiment will approach the actual probability