Sullivan Algebra and Trigonometry: Section 14.3 Objectives of this Section Construct Probability Models Compute Probabilities of Equally Likely Outcomes Utilize the Addition Rule to Find Probabilities Compute Probabilities Using Permutations and Combinations

An event is an outcome from an experiment. The probability of an event is a measure of the likelihood of its occurrence. A probability model lists the different outcomes from an experiment and their corresponding probabilities.

Determine the sample space resulting from the experiment of rolling a die. To construct probability models, we need to know the sample space of the experiment. This is the set S that lists all the possible outcomes of the experiment. S = {1, 2, 3, 4, 5, 6}

The probability of each outcome in the sample space S = {e 1, e 2, …, e n } has two properties: The probability assigned to each outcome is non-negative and at most 1. The sum of all probabilities equals 1.

Probability for Equally Likely Outcomes If an experiment has n equally likely outcomes, and if the number of ways an event E can occur is m, then the probability of E is

A classroom contains 20 students: 7 Freshman, 5 Sophomores, 6 Juniors, and 2 Seniors. A student is selected at random. Construct a probability model for this experiment.

Theorem Additive Rule

What is the probability of selecting an Ace or King from a standard deck of cards?

Probabilities of Complementary Events If E represents any event and represents the complement of E, then Suppose the probability that a hurricane hits a county in a given year is Find the probability that a hurricane doesn’t hit the county. Since there are only two possible events in the sample space, hurricane or no hurricane, these events are complementary. Prob(No H) = 1 - Prob(H) = = 0.98

Suppose you managed a little league team. You have 8 pitchers, 10 fielders, and 5 other players on the bench. If you choose three players at random, what is the probability that they are all pitchers? Prob(3 Pitchers) = # of ways to choose 3 pitchers # of ways to choose 3 players

Prob(3 Pitchers) = # of ways to choose 3 pitchers # of ways to choose 3 players