Theoretical probability (P) equals the number of favorable outcomes divided by the total number of possible outcomes. The value of P will always be between 0 and 1. A value of 0 means the chance of the event occurring is impossible while a value of 1 means it's certain to occur. If a man flipped a coin 50 times and it landed on heads 20 times, the theoretical probability of landing on heads would be 20 divided by 50, or 40 percent.
The value of P is ultimately just an approximation or estimate, which is why a large number of trials or experiments are required for it to be precise. If one wanted to determine the theoretical probability of a flipped coin landing on heads, for instance, he would have to flip a coin hundreds of times, before using the P equation, to calculate the theoretical probability.
In theoretical probability, the sample space refers to all the possible outcomes for an experiment. If flipping a coin, the sample space would include heads and tails. If rolling a die, however, the sample space would consist of 1, 2, 3, 4, 5 and 6. An event refers to a specific outcome. If one wanted to roll an even number, for example, the event would include 2, 4 and 6.
Other forms of probability include experimental probability and subjective
probability. The former is based on observations obtained from legitimate experiments,
whereas the latter is simply based on intuition.