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.

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Sampling Table

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