Sets and Probability Sets Sets Set a well

Sets and Probability Sets

Sets ¡ Set- a well defined collection of objects in which it is possible to determine if a given object is included in the collection. l ¡ A set consisting of the numbers 2, 4, and 7 is written as {2, 4, 7} Elements (or Members) – the numbers belonging to a set. The numbers 2, 4, and 7 are called the elements or members of the above set. l To show that the number 2 is a member of the set, we write 2 {2, 4, 7} l Likewise to show that a number 8 is not a member of the set we write 8 {2, 4, 7}

Sets ¡ Other Notation l A B means that set A is a SUBSET of set B. That is, every element of A is also an element of B. ¡ l l l We can determine the number of subsets for each set by 2 n. A B means that set A is a PROPER SUBSET of set B. That is, every element of A is also an element of set B, but set A and set B are not exactly the same. Intuitively, A B means that A is not a subset of B. The symbol 0 represents the number zero. The symbol represents a set with no elements – an empty set – a null set. A and A A. That is the empty set is a subset of any set and every set is a subset of itself. The letter U represents the universal set which includes all objects being discussed.

Sets/Venn Diagrams ¡ A as a subset of B (A B) B A U

Sets/Venn Diagrams ¡ The Complement of A (A’) l If the universal set U is {1, 3, 5, 7, 9} ¡ If A = {1, 5, 7} then A’ = {3, 9} A’ A

Sets/Venn Diagrams ¡ Intersection of Two Sets (A B) l If A = {2, 4, 6, 7} and B={1, 2, 5, 7} ¡ A Then A B = {2, 7} AB A AB DISJOINT SETS A B =

Sets/Venn Diagrams ¡ Union of Two Sets (A B) l If A = {2, 4, 6, 7} and B={1, 2, 5, 7} ¡ Then A B = {1, 2, 4, 5, 6, 7} B A DISJOINT SETS A B={1, 2, 4, 5, 6, 7}

Applications of Venn Diagrams ¡ Union Rule For Sets n(A B) = n(A) + n(B) – n(A B) A ¡ B Union Rule For Disjoint Sets n(A B) = n(A) + n(B) A B

Introduction To Probability ¡ Terms l l l Experiment – activity or occurrence with an observable result Trial – each repetition of an experiment Outcomes – possible results of each trial Sample Space – set of all possible outcomes for an experiment Event – a subset of a sample space

Introduction To Probability ¡ Terms, con’t l ¡ Mutually Exclusive – when two events cannot occur at the same time Probability Rules l l 0 < P(E) < 1 P(E) = 1