In a school celebration for excellently-performing students, the probability that
Minister of Education attends is 0.65, the probability that the vice principal of
the school attends is 0.51, and the probability that both attend is 0.3. Find the
probability that at least one of them attends.
In this case, event is the Minister of Education attending the school celebration, and event is the vice principal of the school attending. The notation refers to the probability of either event or event occurring, or both. In other words, the notation refers to the probability of at least one of the events occurring.
If and are two non-mutually exclusive events, then , where the notation refers to the probability of events and occurring together.
First, use this fact to determine .
Thus, the probability that at least one of them attends the school celebration is 0.86.