1. INTRODUCING PROBABILITY

2. This is denoted with an S and is a set whose elements are all the possibilities that can occur A probability model has two components: A sample space and an assignment of probabilities. Each element of S is called an outcome. A probability of an outcome is a number and has two properties: 1. The probability assigned to each outcome is nonnegative. 2. The sum of all the probabilities equals 1.

3. Let's roll a die once. S = {1, 2, 3, 4, 5, 6} This is the sample space---all the possible outcomes probability an event will occur What is the probability you will roll an even number? There are 3 ways to get an even number, rolling a 2, 4 or 6 There are 6 different numbers on the die.

4. The word and in probability means the intersection of two events. What is the probability that you roll an even number and a number greater than 3? E = rolling an even number F = rolling a number greater than 3 How can E occur? {2, 4, 6} How can F occur? {4, 5, 6} The word or in probability means the union of two events. What is the probability that you roll an even number or a number greater than 3?

5. ADDITION RULE For any two events E and F, P(E  F) = P(E) + P(F) - P(E  F) Let's look at a Venn Diagram to see why this is true: EF If we count E and then count F, we've counted the things in both twice so we subtract off the intersection (things in both). EF

6. ADDITION RULE for Mutually Exclusive Events If E and F are mutually exclusive events, P(E  F) = P(E) + P(F) Let's look at a Venn Diagram to see why this is true: EF Mutually exclusive means the events are disjoint. This means E  F =  You can see that since there are not outcomes in common, we won't be counting anything twice.

7. E This is read "E complement" and is the set of all elements in the sample space that are not in E Remembering our second property of probability, "The sum of all the probabilities equals 1" we can determine that: This is more often used in the form If we know the probability of rain is 20% or 0.2 then the probability of the complement (no rain) is 1 - 0.2 = 0.8 or 80%

8. Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. www.slcc.edu Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum.www.mathxtc.com Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au