LESSON 3

Sample Space

Denoted by S; the set containing all _ outcomes of a process

Sample Point

Each _ of the sample space S

Event

A _ of a sample space S

Complement

Denoted A'; the subset of all elements of S that are _ in A

Intersection

A ∩ B; contains all elements _ to both A and B

Union

A ∪ B; contains all elements belonging to A _ B or both

Mutually Exclusive

Two events A and B where A ∩ B equals _

Null Set

Denoted by _; contains no elements

Finite Sample Space

Sample space with a _ number of outcomes

Countably Infinite

Outcomes can be listed but go on _

Uncountably Infinite

Outcomes form a _

Multiplication Rule (Counting)

If operation 1 has n1 ways and operation 2 has n2 ways, together they have _ ways

Number of Arrangements of n Objects

According to the multiplication rule, equals _

Permutation

An arrangement of all or part of a _ of objects

Permutation Theorem 1

Number of permutations of n distinct objects taken r at a time: _

Permutation Theorem 2

Distinct permutations of n things of which n1, n2,… nk are of each kind: _

Permutation Theorem 3

Number of ways to partition n objects into r cells: _

Combination (Theorem 4)

Number of combinations of n distinct objects taken r at a time: _

Probability Range

P(A) must satisfy _ ≤ P(A) ≤ _

P(∅)

Probability of the null set equals _

P(S)

Probability of the entire sample space equals _

Equally Likely Outcomes

P(A) = number of favorable outcomes divided by _

Additive Rule

P(A ∪ B) = P(A) + P(B) minus _

Additive Rule (Mutually Exclusive)

If A and B are mutually exclusive, P(A ∪ B) = _

Complement Rule

P(A') equals _

Partition of S

A collection of mutually exclusive events whose _ equals S

Conditional Probability

P(B|A) = P(A ∩ B) divided by _, provided P(A) > 0

Conditional Probability Notation

P(B|A) is read as "probability of B _ A"

Multiplication Rule (Probability)

P(A ∩ B) = P(A) times _

Independent Events (Condition)

A and B are independent if P(B|A) equals _

Independent Events (Multiplication)

For independent A and B, P(A ∩ B) = _

Dependent Events

The outcome of one event _ the probability of the other

Marginal Probability

Probability of a single event occurring _ other events

Total Probability / Rule of Elimination

P(A) = sum of P(Bi) times _ for all partitions Bi

Bayes' Rule

Used to find the probability of _ given that event A occurred