Statistics Ch 4

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Section 4.1

Construct sample spaces

Probability - proportion of times an event occurs

Law of Large Numbers - If a probability experiment is repeated again and again, the proportion of times that a given event occurs will approach its probability

Sample space - contains all possible outcomes of a probability experiment

Event - an outcome or a collection of outcomes from a sample space

Probability model - consists of a sample space, along with a probability for each event

Compute and interpret probabilities

Computing probabilities with equally likely outcomes: P(A) = (Number of outcomes in A)/(Number of outcomes in the sample space) = k/n

0</=P(A)</=1

Unusual event - probability is small

Approximate probabilities by using the Empirical Method

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Section 4.2

Compute probabilities by using the General Addition Rule

Compound event - formed by combining two or more events (coin toss and die roll)

P(A or B) = P(A occurs or B occurs or both occur)

Contingency table - categorizes people based on two variables

General Addition Rule: P(A or B)=P(A)+P(B)-P(A or B)

Compute probabilities by using the Addition Rule for Mutually Exclusive Events

Mutually exclusive - it is impossible for both events to occur at the same time

The Addition Rule for Mutually Exclusive Events: P(A or B)=P(A)+P(B)

Compute probabilities by using the Rule Complements

Complement - if A occurs then the complement is when A does not occur (i.e. the complement of "rain" is "no rain" denoted A^c

Rule of Compliments: P(A^c)=1-P(A)

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Section 4.3

Compute conditional probabilities

Conditional probability - probability that is computed with the knowledge of additional info

Unconditional probability - probability computed without such knowledge

General Method for Computing Conditional Probabilities:

P(B|A)=P(A and B)/P(A)

Compute probabilities by using the General Multiplication Rule

General Multiplication Rule:

P(A and B)=P(A)P(B|A)

Compute probabilities by using the Multiplication Rule for Independent Events

Independent - an event's occurrence is not affected by a different event

Dependent - the opposite

Multiplication Rule for Independent Events

P(A and B)=P(A)P(B)

Sampling with and without replacement

Compute the probability that an event occurs at least once