P&S L2 C2 S3

Two events are mutually exclusive if both cannot happen at the same time. In the first picture, if any element of set A is chosen, then it cannot be in B. The event A excludes B. In the second picture the two events overlap. This means that BOTH events can happen at the same time. There are some elements which are members of both sets A and B at the same time. These are NOT mutually exclusive events.

AXIOM: For mutually exclusive events, the probability that either one of the two happens is the SUM of their separate probabilities.

Let U be the population of 100 students, and R a random draw from U. Consider the set A of all students who have pierced ears -- suppose that this is 25 students. Consider the set B of all male students. Suppose that this is 60 students. These sets will be mutually exclusive if no male student has pierced ears. In this case, the following addition law for probabilities holds:

In words, this means that the probability that a randomly chosen element R belongs to either one of the two sets (MALES or Pierced Ears) -- that is either R is male or R has pierced ears -- this probability is the SUM of the two separate probabilities P(A)= 25/100 and P(B)=60/100. This is true BECAUSE the two sets A and B are mutually exclusive: If you are male you dont have pierced ears, and if you have pierced ears, you are not male