Vocabulary

Independent events: Events for which the occurrence of one has no impact on the occurrence of the other.

Relative frequency: The number of times an outcome occurs divided by the total number of trials.

Sample space: All possible outcomes of a given experiment.

Event: A subset of a sample space.

Simple Event: An event consisting of just one outcome. A simple event can be represented by a single branch of a tree diagram.

Compound Event:  A sequence of simple events.

Complement: The complement of event E, sometimes denoted E′ (E prime), occurs when E doesn’t. The probability of E′ equals 1 minus the probability of E: P(E′) = 1 – P(E).

Counting Principle: If an event A can occur in m ways and for each of these m ways, an event B can occur in n ways, then events A and B can occur in ways. This counting principle can be generalized to more than two events that happen in succession. So, if for each of the m and n ways A and B can occur respectively, there is also an event C that can occur in s ways, then events A, B, and C can occur in ways.

Tree diagram: A tree-shaped diagram that illustrates sequentially the possible outcomes of a given event.    

**Complement of a Set: The collection of all items not in a set

**Element: A member or item in a set

**Intersection of Sets: The set of all elements contained in all of the given sets

**Null Set: : A subset that does not contain every element of the parent set

**Proper Subset: A subset that does not contain every element of the parent set

**Set: A collection of numbers, geometric figures, letters, or other objects that have some characteristic in common

**Subset: A collection of items drawn entirely from a single set. A subset can consist of any number of items from a set ranging from none at all (a null subset) all the way up to the entire set (every set is a subset of itself).

**Union of Sets: The set of all elements that belong to at least one of the given two or more sets

**Venn Diagram: A picture that illustrates the relationship between two or more sets

**{ }: “Curly braces” are often used to denote members of a set. For example, the positive, single-digit, even numbers are 2,4,6,8.

**Î: Is an element of – For example, if A is the set of positive, single-digit, even number, then 2 Î A.

**Ï: Is not an element of – For example, if A is the set of positive, single-digit, even number, then 3ÏA.

**Ì: Is a subset of – For example, if A is the set of positive, single-digit, even number, then 2 Ì A. NOTE: Many authors and texts use this symbol only for proper subsets, but some are not so precise.

**Í: Is a subset of – The difference between and is similar to the difference between < and <. For example, if A is the set of positive, single-digit, even number, then 2,4,6,8 Í A. NOTE: While 2,4,6,8 is a subset of A, it is not a proper subset of A.

**È: Union – For example, if B is the set of even numbers and C is the set of odd numbers, then BÈC=Integers.

**Ç: Intersection – For example, if D is the set of non-negative numbers and E is the set of non-positive numbers, then DÇE = 0

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