Probability Chapter 1 Flashcards
Define the 3 criteria required for {G1,G2,G3} to form a partition of the sample space?
Gi n Gi =empty set for all i≠I
G1 U G2 U G3=S1 the sample space
P(Gi)>0 for all I
What is an experiment?
An experiment is any process that requires some action to be performed and had an outcome that can be recorded
What is an outcome?
An outcome is any single result from an experiment?
What is a sample space?
A sample space is the set (collection) of all possible outcomes of an experiment & is typical denoted by S.
What is an event?
An event is any collection of outcomes from the sample space. More formally it is a subset of the sample space. Events are typically denotes by capital letters.
What is a null event?
The null event (or empty set) contains no outcomes & is denoted by Ø
What are the definitions of 2 events A & B?
Intersection (AnB)- both A & B occur
Union (AuB)- either A or B or both occur
Complement (Ā)- not A, occurs when A does not
Disjoint (AnB= Ø)- A & B have no points in common, so if A happens then B does not
Subset (A ⊂ B)- if A happens then B will definitely happen. Also known as A implied B.
What are permutations?
Permutations is where order matters!!!
The number of possible permutations (orderings) of the r objects from n is
^nPr= n!/(n-r)!
What are combinations?
Combinations is where order doesn’t matter!!!
Suppose there are a collection of n objects all of which are different. Then they are
^nCr= n!/(n-r)!r!
Possible combinations
What is the probability of any single outcome?
If an experiment has a sample space of n outcomes that are equally likely to occur, the probability of any single outcome is
P(any single outcome)=1/n
How do you calculate P(AuB)?
P(AuB)=P(A)+P(B)-P(AnB)
- If A & B are disjoint then P(AnB)=0
- If B is a subset of A then P(AnB)=P(B)
- If A & B are independent then P(AnB)=P(A)P(B)
How do you find the probability of A happening given that B has already happened (conditional probability)?
P(A\B)=P(AnB)/P(B)
What is the Bayes theorem?
Bayes theorem can be based on the idea of a partition, which is a set of events that follow 3 rules
