UMD STAT 400 ( copy)

Sample Space

The set of all possible outcomes of an experiment, denoted by S

Union

All outcomes in either A, B, or both A and B. Denoted P(A ∪ B),

Intersection

All outcomes in both A and B. Denoted P(A ∩ B)

Complement

Set of all outcomes not contained in A. Denoted P(A')

Null

No outcomes. Denoted ¤

Mutually Exclusive

If P(A ∩ B) = ¤, they are said to be mutually exclusive, for they share no outcomes

Simple Probability Formula

Number of wanted (favorable) outcomes / Number of total outcomes

Empirical Probability

Ratio of number of event occurrences to the number of trials

Relative Frequency

Same as empirical probability

Axioms of Probability

1. P(A) ≥ 0

2. P(S) = 1

3. A1, A2, ... infinite disjoint events: P(A1 ∪ A2...) = Summation

P(A ∪ B) = ?

P(A) + P(B) - P(A ∩ B)

P(A ∪ B ∪ C) = ?

P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)

Tree Diagram

Used

Permutation

Ordered Subset (e.g. poker straight

Combination

Unordered Subset (e.g. poker three of a kind)

n choose k = ?

n! / k! (n - k)!

Conditional Probability

Probability of A given B. Denoted P(A | B)

P(A | B) = ?

P(A ∩ B) / P(B)

Multiplication Rule

P(A ∩ B) = P(A | B) * P(B)

Bayes' Theorem

When mutually exclusive, and P(B) = 0, P(Aj | B) = P(Aj ∩ B) / P(B)

Independence of Events

P(A | B) = P(A); B has no bearing on events

P(A ∩ B) = ?

P(A)P(B) only when both are independent