Probability Rules

We now develop some important rules for computing probabilities for compound events. The development begins by defining A as an event in the sample space, S, with A and its complement, , being mutually exclusive and collectively exclusive.

Complement Rule
Let A be an event andits complement. Then the complement rule is

 Example: Fairselect Inc. is hiring managers to fill four key positions. The candidates are five men and three women. Assuming that every combination of men and women is equally likely to be chosen, what is the probability that at least one women will be selected?

Solution: We will solve this problem by first computing the probability of the complement of A, “No woman is selected,”  and then using the complement rule to compute the probability probabilities of one through three women being selected. Using the method of classical probability,and, therefore, the required probability is

The Addition Rule of Probability

Let A and B be two events. Using the addition rule of probabilities, the probability of their union is

Example: Product Selection (Addition Rule)
A hamburger chain found that 75% of all customers use mustered, 80% use ketchup, and 65% use both. What is the probability that a customer will use at least one of these?

Solution: Let A be the event “Customer uses mustard” and B the event “Customer uses ketchup.” Thus, we have