Two or more events are said to be mutually exclusive if the occurrence of any one of them means the others will not occur (That is, we cannot have 2 or more such events occurring at the same time).For example, if we throw a 6-sided die, the events "4" and "5" are mutually exclusive. We cannot get both 4 and 5 at the same time when we throw one die.
If E1 and E2 are mutually exclusive events, then E1 and E2 will not happen together. So the probabality of the 2 events will be zero:P(E1 and E2) = 0.Now, suppose "E1 or E2" denotes the event that "either E1 or E2 both occur", then(a) If E1 and E2 are not mutually exclusive events:
P(E1 or E2) = P(E1) + P(E2) − P(E1 and E2)We can also write:P(E1 ∪ E2) = P(E1) + P(E2) − P(E1 ∩ E2)