# Probability

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Probability

## 3. Definitions

### 3.1. Sample Space

3.1.1. With Replacement

3.1.2. Without Replacement

### 3.2. Simple Event

3.2.1. Sum of all Simple Events = 1

3.2.2. If equally likely then probability = 1/k

## 4. Rules for Finding Probabilities

### 4.1. Rule 1 (Not the event)

4.1.1. Probability an event does not occur

4.1.1.1. P(A)+P(A^c)=1

4.2.1. Probability that either of two events happens

4.2.1.1. Rule 2a (general)

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

4.2.1.2. Rule 2b (mutually exclusive events)

4.2.1.2.1. P(A or B)=P(A)+P(B)

### 4.3. Rule 3 (Multiplication)

4.3.1. Probability that two or more events occur together

4.3.1.1. Rule 3a (general)

4.3.1.1.1. P(A and B)=P(A)PB|A)=P(B)PA|B)

4.3.1.2. Rule 3b (independent events)

4.3.1.2.1. PA and B)=P(A)P(B)

4.3.1.3. Rule 3b (extension)

4.3.1.3.1. P(A1 and A2...and An)=P(A1)P(A2)...(PAn)

### 4.4. Rule 4 (Conditional Probability)

4.4.1. Determining a conditional probability

4.4.1.1. P(B|A)=P(A andB)/P(A)

## 8. Events

### 8.5. Conditional Probablity

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

## 10. Strategies

### 10.1. Bayes Rule

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