Question

What is the difference between empirical and theoretical probability?

Answer 1

We know that empirical probability is based on experimental data, which is repeated many number of times. And theoretical probability on the other hand, is purely theoretical and based on our knowledge of that experiment.

Complete step-by-step answer:
We know that probability is the measure of how likely or unlikely is the occurrence of any event or experiment. When the probability is high, that means that an event is more likely to happen, and if the probability is low, then there are less chances of that event to occur. We know that the value of a probability is always greater than or equal to 0, but less than or equal to 1.
We also know that the empirical probability refers to a probability that is based on historical data and past experiments. We are aware that this type of probability is determined on the basis of the results of an experiment repeated many times.
We are very aware that in theoretical probability, on the other hand, we use the knowledge of a situation to calculate the probability. Thus, we can say that theoretical probability is the probability that is determined on the basis of reasoning.
Let us try to understand this with the help of an example. Suppose a coin is flipped 4 times, and we got 1 head and 3 tails. So, the probability of getting a head, in this case, is empirical and its value is $\dfrac{1}{4}$. But, we know that when a coin is tossed, the probability to get a head is $\dfrac{1}{2}$. This is theoretical probability.

Note: We must remember that empirical probability is also called experimental probability. Also, we must know that the value of empirical probability may or may not be equal to theoretical probability. But, when the experiment is repeated a large number of times, then empirical probability tends to close up on theoretical probability.