# Probability

# Probability

by David Warwick
# 1. Types of Events

## 1.1. simple event

## 1.2. mutually exclusive events

### 1.2.1. disjoint event

## 1.3. independent events

## 1.4. dependent events

## 1.5. complementary event

# 2. Interpretations of Probability

## 2.1. relative frequency

## 2.2. personal probability

### 2.2.1. subjective probability

## 2.3. coherent probabilities

# 3. Key Definitions

## 3.1. random circumstance

## 3.2. sample space

## 3.3. conditional probability of the event B, given that the event A occurs: P(A|B)

## 3.4. tree diagram

## 3.5. event

## 3.6. complement

# 4. Probability Rules

## 4.1. Rule 1: "not the event"

## 4.2. Rule 2: addition rule for "either or"

### 4.2.1. Rule 2a: general

### 4.2.2. Rule 2b: mutually exclusive events

## 4.3. Rule 3: multiplication rule for "and"

### 4.3.1. Rule 3a: general

### 4.3.2. Rule 3b: independent events

### 4.3.3. Extension of Rule 3b: more than two independent events

## 4.4. Rule 4: conditional probability

## 4.5. Bayes Rule: finding P(A|B) using P(B|A)

## 4.6. Sample with replacement

## 4.7. Sample without replacement