12.3 Probability of Equally Likely Outcomes

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. 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.

Determine the sample space resulting from the experiment of rolling a die.

Properties of Probabilities

Theorem 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

Thus, if S is the sample space of this experiment, then

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.

For any two events E and F Theorem Addition Rule For any two events E and F if E and F are mutually exclusive events. (mutually exclusive means ).

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

Computing Probabilities of Complementary Events If E represents any event and E represents the complement of E, then

Determine the probability of having 3 girls in a 3 child family. All possibilities are as follows: BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG (where B=boy, G=girl)