Types of Probability

Probability can be calculated in two ways. Based on this there are two types of probability.

Theoretical Probability

When probability is calculated without actually performing the experiment, the probability is called Theoretical Probability. In this type of probability, you calculate the total number of possible outcomes of an experiment (called the sample space) and the number of favorable outcomes (the kind of outcomes of which you are calculating the probability). Their ratio is called the theoretical probability.

For example, suppose you want to know the probability of getting an even number on rolling a number cube. We know that there are a total of six faces on a number cube and three even numbers on it. Thus the total number of possible outcomes is 6 while the number of favorable outcomes is 3. Thus the theoretical probability is,

P(even number) = `3/6 = 1/2`

Experimental Probability

When the probability is calculated based on the results of an experiment, the probability is called experimental probability. Experimental probability can vary from experiment to experiment, since all experiments may not have the same results.

In the same example above, in order to calculate the probability of getting an even number on rolling a number cube, you will actually perform the experiment for a fixed number of times. Suppose you roll the number cube ten times and get an even number four times. Thus, the experimental probability is,

P(even number) = `4/10 = 2/5`

In general, experimental probability is quite close (or sometimes equal) to the theoretical probability unless the experiment is biased. For example, in the above examples, the theoretical probability is 0.5 while the experimental probability is 0.4 which is a number near to 0.5.