June 26, 2019

Chapters

**0 ≤ p(A) ≤ 1**

**p(S) = 1**

### Probability Formula

### Addition Rule

If A B ≠ .

**p(A ∪ B) = p(A) + p(B) − p(A
B)**

**p(A ∪ B ∪ C) = p(A) + p(B) + p(C) − p(A
B) − p(A
C) − p(B
C) + p(A
B
C)**

### Multiplication Rule

## Independent Events

**p(A
B) = p(A) · p(B) **

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## Dependent Events

**p(A
B) = p(A) · p(B|A)**

### Conditional Probability

## Independent Events

**p(A|B) = p(A)**

## Dependent Events

**p(A|B) ≠ p(A)**

### Law of Total Probability

**p(B) = p(A _{1}) · p(B|A_{1}) + p(A_{2}) · p(B|A_{2 }) + ... + p(A_{n}) · p(B|A_{n }) **

### Bayes' Theorem

### Expected Value

## Variance of a Discrete Random Variable

## Standard Deviation of a Discrete Random Variable

### Binomial Distribution

### Normal Approximation to the Binomial

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