Sometimes, we need to deal with two or more events. These are called compound events. A compound event is an event that combines two or more simple events. When this happens, we need a special notation.
Given events A and B:
- The probability that A and B occur is P(A ∩ B) = P(A and B)
- The probability that either A or B occurs is P(A ∪ B) = P(A or B)
Understanding why we use the set notation for these compound events is very important. Remember how we represented events in a universe using circles earlier? Let's say that our universe is 100 people who showed up for an experiment in which a new test for cancer is being developed:
In the preceding diagram, the red circle, A, represents 25 people who actually have cancer. Using the relative frequency approach, we can say that P(A) = number of people with cancer/number of people in study, that is, 25/100 = ¼ = .25. This means that there is a 25% chance that someone has cancer.
Let's introduce a second event...