Mutually exclusive events
- If event A and event B can’t occur simultaneously, then they are called mutually exclusive events.
- If two events are mutually exclusive, then the probability of both occurring is denoted as P (A ∩ B) and
P (A and B) = P (A ∩ B) = 0 - If two events are mutually exclusive, then the probability of either occurring is denoted as P (A ∪ B)
P (A or B) = P (A ∪ B)
= P (A) + P (B) − P (A ∩ B)
= P (A) + P (B) − 0
= P (A) + P (B)
Example: The chance of rolling a 2 or 3 on a six-faced die is P (2 or 3) = P (2) + P (3) = 1/6 + 1/6 = 1/3
Not Mutually exclusive events: If the events are not mutually exclusive then
P (A or B) = P (A ∪ B) = P (A) + P (B) − P (A and B)