# Basic probability rules

(review probability notation here)

##### 1. Complementation rule

For an event A and its complement AC:

### Example:

A = throwing a double six with two dice

AC = not throwing a double six

P(A) = 1/36

P(AC) = 35/36

##### 2. Addition rule

For mutually exclusive events Ai:

### Example:

A1 = the next patient in a hospital is suffering from breast cancer

A2 = the next patient in a hospital is suffering from prostate cancer

P(A1) = 3%

P(A2)  = 2.5%

P(A1EA2) = 5.5%

### Example:

A = a person walking by a shop enters the shop

B|A = person in shop purchase something

C|A B = person buying spends >\$100

P(A) = 10%

P(B|A) = 40%

P(C|A B) =  25%

P(A B C) = 10%*40%*25% = 1%

P(A|B) = 100%

Rearranging the formula leads to Bayes formula;

This formula is of fundamental importance in statistics and is the cornerstone of Bayesian inference.

(More on conditional probabilities)

##### Independence

If A and B are such that

they are called independent events.

### Example:

A = theme park has a bad summer in Miami due to weather

B = theme park has a bad summer in Brussels due to weather

If there is no link between weather in Miami and Brussels then these events are independent. It would be important to know if there is any correlation if you owned both theme parks, because you could have a higher (positive correlation) or lower (negative correlation) probability of a bad summer in both at the same time with a greater resultant cashflow uncertainty.

Read on: Conditional probability

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