P&s 1

Front 1

Basic axioms of probability

Back 1

P{A} >= 0

P{S} = 1

P{U A_k} = sum P{A_k}

Hint 1

Non-negativity

Norming

Sigma-additivity

Front 2

Properties of probability

Back 2

P{©} = 0

P{A°} = 1 - P{A}

AєB --» P{A} <= P{B}

P{AUB} = P{A} + P{B} - P{A and B}

· A1є А2 є ... --» P{U A_k} = lim(P{A_k})

·... є А2 є А1--» P{U°A_k} = lim(P{A_k})

Hint 2

Empty set

Complement

Monotonicity

Sum rule

Continuity (below & above)

Front 3

General inclusion-exclusion formula

Back 3

Hint 3

парні непарні

Front 4

Independence

Back 4

Hint 4

whichever elements we take they are mutually independent

Front 5

Probability product rule

Back 5

P{A and B} = P{A|B} · P{B}

Hint 5

from definition of conditional probability

Front 6

Partition rule

Back 6

Events E_1,..., E_n form a partition of the sample space S if:

** their union = S

** they are pairwise disjoint

Front 7

Total probability rule

Back 7

Hint 7

If B_1,...B_n form a partition of S...

Front 8

Bayes' formula

Back 8

* sum P{A|B}·P{B} = P{A} by total probability rule

Front 9

Generalized total probability rule

Back 9

Hint 9

C