Combining Events

There are two main ways we combine events: "or" and "and".

P(A or B) means that either A happens OR B happens OR they both happen.  For example, select a person at random. What is the probability that s/he is Protestant or a CEO?  The event "A or B" occurs if the selected person is Protestant, if they are a CEO, or if they are both Protestant and a CEO.  

To calculate P(A or B) use P(A) + P(B) - P(A and B)

P(A and B) means BOTH A and B happen simultaneously.  For example, the event "Protestant AND a CEO" occurs only if the selected person is both Protestant and a CEO.

The basic way of computing P(A and B) is, assuming your sample space has equally likely outcomes:  Number of outcomes in both A and B divided by the total number of outcomes in the sample space.

But there are two important "short cuts"

If A and B are mutually exclusive:  P(A and B) = 0.  Also, if P(A and B) = 0, then A and B are mutually exclusive.

If A and B are independent, then P(A and B) = P(A) * P(B).  Also, if P(A and B) = P(A) * P(B) , then A and B are independent.