Probability

1. Interpretations of Probability

1.1. relative frequency

1.2. personal probability

1.2.1. subjective probability

1.3. coherent probabilities

2. Key Definitions

2.1. random circumstance

2.2. sample space

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

2.4. tree diagram

2.5. event

2.6. complement

3. Types of Events

3.1. simple event

3.2. mutually exclusive events

3.2.1. disjoint event

3.3. independent events

3.4. dependent events

3.5. complementary event

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