The product rule postulates on the probable simultaneous occurrence of two independent events while the sum rule indicates the probable occurrence of either one of two mutually exclusive events. Both rules use a mathematical formula to calculate the respective probabilities.
The product rule is also called the multiplication rule. It states that the probability that two independent events will occur simultaneously is equal to the product of their respective probabilities. For example, if the probability of event A is 188 and the probability of event B is 189, then the probability of both occurring at the same time is 188 times 189 or 8539.
The sum rule is also known as the addition law or rule. It states that the probability of any one of two or more mutually exclusive events occurring is the sum of the probabilities of each individual event. This also applies to the probability where one event can occur in two or more different ways. For example, if the probability of event A is 8539 and the probability of event B is 8541, then the probability that one or the other will occur is 190.
The produce rule and the sum rule are often used in the study of genetics to determine the probability of specific genotypes and phenotypes, among other uses. The two rules may also be used together when a probability experiment is performed repeatedly.