Difference Between Empirical Probability and Theoretical Probability
Empirical probability defines a probability value gained from experimenting. For example, we want to find out the probability of getting an even number when dice are tossed. To find the probability, we will perform an experiment in which we will toss the dice 100 times and calculate the probability from there.
Empirical Probability = Number of times an event occurred / Total number of trails
Suppose we obtained 60 times an even number during tossing of the dice 100 times, the probability will then be:
P(H) = 60 / 100 = 0.6
Therefore, there is a 0.6 likelihood of obtaining an even number when a dice is tossed 100 times. On the other hand, theoretical probability comes into play when it is not feasible to experiment to determine probability. Then we assume the outcomes of an event are all equally likely. For example, we want to find out whether we obtain an even number when a coin is tossed. When a dice is tossed, there is a 50/50 chance of obtaining an even number or an odd number. Then the probability will be:
P(E) = number of successful outcomes of the event / total number of outcomes
Here, the total number of outcomes is 6, and the number of successful outcomes will be 3(i.e, 2, 4, 6) therefore the probability of occurrence of an even number is:
P(T) = 3 / 6 = 1 / 2 = 0.5
Therefore, there is a 0.5 likelihood of obtaining an even number when a dice is tossed. So finally we can conclude that theoretical probability is based on the assumption that outcomes have an equal chance of occurring while empirical probability is based on the observations of an experiment.
Empirical Probability
Empirical Probability: Probability describes the chance that an uncertain event will occur. Empirical probability is based on how likely an event has occurred in the past. It is also called experimental probability. It is based on the relative frequency approach. We can get our results from experience rather than from a theory.
We employ the empirical probability-generating function in constructing a goodness-of-fit test for negative binomial distributions. In empirical probability, the experimental conditions may not remain the same for all repetitions of that experiment. In statistical terms, the empirical probability is just an estimate of an event.
Table of Content
- Empirical Probability Meaning
- Difference Between Empirical Probability and Theoretical Probability
- Empirical Probability Examples
- Advantages of Empirical Probability
- Disadvantages of Empirical Probability
- Summary – Empirical Probability