Sets A set is simply any collection of objects A set may be finite or infinite A set with nothing in it is called the empty set (null or void set) and is denoted, { } or ø Two sets are equal if they have exactly the same elements

Subsets If A={1,2,3} is a set then subsets of A include the sets:{ },{1},{2},{3},{1,2}, {1,3},{2,3},{1,2,3}

Sample Space The set, S, of all distinct possible outcomes of an experiment is called a sample space.

What is the sample space for a roll of a single six-sided die?

Events (E) An event is any collection of outcomes of a probability experiment Suppose we are flipping a coin-what are the events that may occur? Suppose we are rolling a die, what are the events that may occur? What if we flip the coin twice, what are the events that may occur?

Probability of an Event Given an event, we would assign it a number, P(E) called the probability of E This number indicates the likelihood that the event will occur. We can find this number by setting up a ratio:

Venn Diagrams The Venn Diagram is made up of two or more overlapping circles or sets. It is often used in mathematics to show relationships between sets.

Venn Diagrams Here is the Venn Diagram associated with the set A.

Complements A complement of A is everything that is in the universal set, U, but not in the set A. The complement is the event that A does not happen. The complement is denoted, Ac. Here is the complement of set A.

Unions of sets The union of sets A and B is the set of all items that are either in A or B. We express union, AB In math, the word “or” also includes members of both A and B.

Intersection of Sets The intersection of sets A and B is the set of all items that are in both A and B. We express intersection, AB.

Properties of Probabilities Probabilities must satisfy the following properties: For any event, E, 0  P(E)  1 If E is certain to happen then P(E)=1 If E and F are events where E and F cannot happen at the same time, then P(E or F) = P(E) + P(F)