Probability and Combinatorics Flashcards

Flashcards for reviewing probability concepts and combinatorics.

Sample Space

The set of all possible outcomes of a statistical experiment.

Sample Point

Members of the sample space, or possible outcomes that can occur.

Proposisi Peluang 1

P(EC) = 1 − P(E)

Proposisi Peluang 2

If E ⊆ F, then P(E) ≤ P(F)

Proposisi Peluang 3

P(E ∪ F)= P(E) + P(F) - P(E ∩ F)

Property 1 of Sets

A ∩ ∅ = ∅

Property 2 of Sets

A ∪ U = U

Property 3 of Sets

A ∩ A' = ∅

Property 4 of Sets

A ∪ A' = S

Property 5 of Sets

S' = ∅

Property 6 of Sets

∅' = S

Property 7 of Sets

(A')' = A

Property 8 of Sets

(A ∩ B)' = A' ∪ B'

Property 9 of Sets

(A ∪ B)' = A' ∩ B'

De Morgan's Law (1)

A \ (B ∪ C) = (A \ B) ∩ (A \ C)

De Morgan's Law (2)

A \ (B ∩ C) = (A \ B) ∪ (A \ C)

Addition Rule

If the events are mutually exclusive, the total number of ways is r₁ + r₂ + … + rₙ.

Multiplication Rule

If events are related, the total number of ways is r₁ × r₂ × … × rₙ.

Permutation of k from n (k ≤ n)

n! / (n - k)!

Permutation with identical elements

n! / (k₁! * k₂! * … * kₜ!)

Cyclic Permutation

(n - 1)!

Combination of k from n (k ≤ n)

n! / ((n - k)! * k!)