Multiplication Rule & Tree Diagrams
Multiplication Rule for Independent Events
If knowing that event A occurs does not change the probability that event B occurs or vice versa, then we can say that events A and B are independent. If two events are independent, then one can calculate the probability that both events occur by using the following formula:
This rule can be expanded beyond just two events. For example, if A, B, and C are all independent events, then the following formula holds true:
Tree diagrams are a powerful tool that allows one to visualize all the possible outcomes of a random activity or experiment. Each branch in a tree diagram represents a possible outcome. Furthermore, once the tree diagram is drawn and outcomes have been established, tree diagrams help one calculate the corresponding probabilities of each outcome.