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Probability
by Jane_l Yang
# Probability

## Random Circumstance

### outcome not determined until
we see it

### Outcome already determined
but our knowledge is uncertain

## Relative Frequency
Interpretation

### Make assumption about
Physical world

### Make direct observation of
how often something
happens over many,
many repetitions of the
situation.

## Number between 0 and 1

### The possible outcome of a
random circumstance

### Meets 1st condition for valid
probablity

## Personal Probability
(subjective)

### Degree an individual believes
it will happen

### Coherent (no contradiction)

## Uses percentages based on
proportions of individuals

## Definitions

### Sample Space

### Simple Event

### Event

## Events

### Complementary ("Opposite")

### mutually exclusive (disjoint)

### Independent

### Dependent

### Conditional Probablity

## Rules for Finding
Probabilities

### Rule 1 (Not the event)

### Rule 2 (Addition)

### Rule 3 (Multiplication)

### Rule 4 (Conditional Probability)

## Philosophical Issue

### Outcome has been
determined but is still
unknown

### Confidence vs Probability

## Strategies

### Bayes Rule

### Two-way Tables:
Hypothetical 100,000

### Tree Diagram

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range from 0 to 5

The proportion of times something would occur over the long run.

With Replacement

Without Replacement

Sum of all Simple Events = 1

If equally likely then probability = 1/k

P(B|A) = probability of B given A

Probability an event does not occur, P(A)+P(A^c)=1

Probability that either of two events happens, Rule 2a (general), P(A or B)=P(A)+P(B)-P(A and B), Rule 2b (mutually exclusive events), P(A or B)=P(A)+P(B)

Probability that two or more events occur together, Rule 3a (general), P(A and B)=P(A)PB|A)=P(B)PA|B), Rule 3b (independent events), PA and B)=P(A)P(B), Rule 3b (extension), P(A1 and A2...and An)=P(A1)P(A2)...(PAn)

Determining a conditional probability, P(B|A)=P(A andB)/P(A)

P(A|B)=P(A and B)/PB|A)P(A)+P(B|A^c)P(A^c)