P1. Probability Basics

Question 1

Complement: notation and meaning

Answer 1

A^c or A’

[set of not A]

Question 2

Intersection: notation and meaning

Answer 2

A∩B

[A and B]

Question 3

Union: notation and meaning

Answer 3

A∪B

[A or B]

Question 4

Define: sample space

Answer 4

The set of Ω.

Set that contains all possible (primitive) outcomes that we are considering.

Question 5

Define: event

Answer 5

A subset of Ω (including Ω itself).

Question 6

Define: event space

Answer 6

Denoted as ℱ

A set of subsets of Ω which must satisfy certain properties. It defines the set of all describable events to which we want to assign probabilities.

Question 7

Define: probability

Answer 7

A probability is a function P that satisfies, for all events in ℱ, the axioms:

P(A)≥0, for all A∈ℱ

P(Ω)=1

If A₁, A₂, … ∈ ℱ are mutually exclusive (disjoint) then P(A₁∪A₂∪…) = P(A₁)+P(A₂)+…

Question 8

What is the first axiom?

Answer 8

P(A) ≥ 0, for all A ∈ ℱ

Question 9

What is the second axiom?

Answer 9

P(Ω) = 1

Question 10

What is the third axoim?

Answer 10

If A₁, A2, … ∈ ℱ are mutually exclusive (disjoint) then P(A1∪A2∪…) = P(A1)+P(A2)+…