The occurrence of one event does not affect the occurrence of the other event.
Mutually Exclusive Events
Events that cannot happen at the same time.
Examples of the Events
Suppose that we are rolling dice and want to know about the chances of rolling a 1 and a 6. If we roll two dice at the same time, the result of rolling the first die does not affect the result of rolling the second die. Therefore, rolling a 1 on the first die and rolling a 6 on the second die is an example of independent events.
Now, if we have only one die, it is not possible to roll a 1 and a 6 at the same time. Therefore, rolling a 1 and rolling a 6 using only one die is an example of mutually exclusive events.
Probability of the Events
Finally, let's compare the probabilities that two events will both occur if the they are independent and if they are mutually exclusive.
Events A and B
P(AandB)
Independent Events
P(AandB)=P(A)* P(B)
Mutually Exclusive Events
P(AandB)=0
When two events are independent, the probability that they both occur is equal to the product of probabilities of each of the events. However, in case of mutually exclusive events, the probability that both of them will occur at the same time must be equal to 0.
