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# Probability And Counting

Logic

* Certainty: Math
* Uncertainty: Probability (numerical representation of uncertainty)

## Naive definitnio of Probability

* A sample space is the set of all possible outcomes of an experiment.
* An event is a subset of the sample space.

\* The concept of a set: to think of probabilities as mathematics.\
\* Probability is not intuitive.

P(A) = # favorable outcomes A / # possible outcomes\
(A = event)

Assumes: all outcomes equally likely finite sample space.

## Counting Principle

* Multiplication Rule: it have experiment with n, possible outcomes, and for each outcomes of 1st experiment there are outcomes for 2nd experiemnt, ..., for each n\_r ... n\_1, n\_2, ..., n\_r overall possible outcomes

## Binomial Coefficient

Subsets of size k, of groups of n people.

![image](https://latex.codecogs.com/gif.latex?\binom{n}{r}%20%3D%20\frac{n!}{\(n-k\)!k!})

## Sampling Table

...