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Statistics
Alternative Chapter 4
32
Mathematics
Undergraduate 2
03/31/2009

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Term
Outcome
Definition
An outcome is the result of an experiment or other situation involving uncertainty.
Term
Sample Space
Definition
The set of all possible outcomes of a probability experiment is called a sample space.
The sample space is an exhaustive list of all the possible outcomes of an experiment. (sometimes S)
Experiment Rolling a die once:
Sample space S = {1,2,3,4,5,6}
Experiment Tossing a coin:
Sample space S = {Heads,Tails}
Experiment Measuring the height (cms) of a girl on her first day at school:
Sample space S = the set of all possible real numbers
Term
Event
Definition
An event is any collection of outcomes of an experiment.

Formally, any subset of the sample space is an event.

Any event which consists of a single outcome in the sample space is called an elementary or simple event. Events which consist of more than one outcome are called compound events.
Term
Symbols to know if A and B are two events in the sample space
Definition

AυB (A union B) = 'either A or B occurs or both occur' A∩B (A intersection B) = 'both A and B occur'

(A is a subset of B) = 'if A occurs, so does B'

A' or A = 'event A does not occur'

Φ(the empty set) = an impossible event

S (the sample space) = an event that is certain to occur

Term
Relative Frequency
Definition

Rule One:

 it is the value calculated by dividing the number of times an event occurs by the total number of times an experiment is carried out

Term
Formula for Rule One: Relative Frequency
Definition

       number of times A occurred      

number of times the trial was repeated

Term
Criteria for Rule One: Relative Frequency
Definition

An approximation is being obtained instead of an exact value;

As the total number of observations ↑,

the corresponding approximations get closer to actual probability;

It can be used for events that do not have equally likely results.

Term
Rule Two: Classical Approach to Probability
Definition
Approach in which the probability of an event is determined by dividing the number of ways the event can occur by the total number of possible outcomes.
Term
Equation for Rule Two: Classical Approach
Definition

number of ways A can occur 

total number of outcomes

Term
Criteria for Rule Two: Classical Approach
Definition
When all outcomes are equally likely, like drawing a name out of a hat
Term
Rule Three: Subjective Probability
Definition
A subjective probability describes an individual's personal judgement about how likely a particular event is to occur. It is not based on any precise computation but is often a reasonable assessment by a knowledgeable person
Term
Criteria for Rule Three: Subjective Prob.
Definition
Is not based on actual, frequent values, but rather expresses an educated guess.
Term
What is the Complement of an event
Definition
All outcomes in which the original outcome does not occur
Term
How to show your data of probabilities
Definition

Give exact fractions or decimals, or round decimals to three significant digits. 

Term
Odds in Favor
Definition
Odds m:n, read as m to n, in favor of an event mean we expect the event will occur m times for every n times it does not occur.
Term
Odds Against
Definition
Odds m:n, read as m to n, against an event mean we expect the event will not occur m times for every n tiems it does occur
Term
Payoff Odds
Definition

The ratio of net profit gained to the amount bet

 

(net profit) : (amount bet)

Term
What is a Compound Event
Definition
Any event combining two or more simple events.
Term
What is the Addition Rule
Definition
The addition rule is a result used to determine the probability that event A or event B occurs or both occur
Term
What is the Formal Addition Rule
Definition

where P(A and B) denotes the probability that A and B both occur at the same time as an outcome in a trial of a procedure.

 

P(A or B) = P(A) + P(B)- P(A and B)

Term
Mutually Exclusive(disjoint) Events
Definition
Two events are mutually exclusive (or disjoint) if it is impossible for them to occur together.
Term
Multiplication Rule
Definition

The multiplication rule is a result used to determine the probability that two events, A and B, both occur.

 

P(A∩B)=P(A)P(B)

 

the probability of the joint events A and B is equal to the product of the individual probabilities for the two events
Term
What is a Tree Diagram
Definition
A picture of the possible outcomes of a procedure.
Term
P(A | B)
Definition
P(A | B) = the conditional probability that event A occurs given that event B has occurred already
Term
P(B | A)
Definition
P(B | A) = the conditional probability that event B occurs given that event A has occurred already
Term
What is an Independent Event
Definition
Events that have no influence on eachother
Term
What is a Dependent Event
Definition
Events for which the occurrence of any one event affects the probabilities of the occurences of the other events.
Term
At Least One Formula
Definition

P(at least one)= 1-P(none)

 

You can find the prob. that NONE of the events will occur, then find the complement

Term
What is a Conditional Probability
Definition
A Conditional Probability of an event is a prob. obtained with the additional information that some other event has already occurred.
Term
What is the Factorial Notation
Definition

N!=n, n-1, n-2, n-3...

 

ex: 4!=4*3*2*1=24

Term
Number of permutations
Definition

nPr =       n!    

           (n- r)! 

 

the number of permutations of r items selected from n different available items

Term
What is the Combination Rule formula
Definition

nCr =         n!      

             (n - r)!r!

 

 

 

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