Math 183 -- Intro to Probability Theory

Study probability for 183

Formula for probability of an event

E = event, S = sample space

WISE protocol

W = define event in (W)ords

IS = event defined (I)n (S)ymbols

E = (E)xpression asked about

(WIS) Let A be the event that most of the class passes the test

(E) P(A) = …….

Phrase the following in words

Probability of A AND B

Phrase the following in words

Probability of A OR B

Phrase the following in words

Probability of A GIVEN B

Formula of the following; NOT DISJOINT

There is an overlap between the two

Formula of the following; DISJOINT

There is no overlap between the two

Formula of the following; INDEPENDENT

Being in one does not affect being in the other

Ratio of A in B is the same as ratio of A in the sample space

Formula of the following; DEPENDENT

Being in one affects being in the other

Ratio of A in B is NOT the same as ratio of A in the sample space

Law of Total Probability

Bayes Theorem

Bayes Theorem (ADV)

Visualizations: Venn Diagram

joint probability = blue

marginal probability = red or green

conditional probability = blue divided by red (or blue divided by green)

Visualizations: Contingency Table

joint probability = red

marginal probability = green

conditional probability = number in a red / number in a green

Visualizations: Tree