STA1000S
Module 1: Probability
Work Unit 1: Introduction to Probability
Equations
number of ways ways of getting selected outcome
P r(outcome) = total number of possible outcomes
payout f or winning number
Win percentage = amount bet across all numbers
× 100
House advantage = 100 − win %
payout
F air payout for a win = win %
expected prof it ∨ loss
% return on amount bet = bet amount
House advantage = − % return
STA1000S 1
, Basics
Roulette uses the numbers 0 → 37
but 0 is 'dead'
There are 37 options
when using probabilities, there are 36 options
Work Unit 2: Set Theory, Probability Axioms &
Theorems
Basics
Sample Space (S)
Universal set
All objects under consideration
Subset ( ⊂ or ⊃)
One set is contained in another set
Empty Set (Ø or {})
Has no members
If the intersection of 2 sets is an empty set:
the sets are mutually exclusive / disjoint
Intersection (∩)
and
The intersection of any 2 sets: the set that contains exactly those elements
which belong to both sets
STA1000S 2
Module 1: Probability
Work Unit 1: Introduction to Probability
Equations
number of ways ways of getting selected outcome
P r(outcome) = total number of possible outcomes
payout f or winning number
Win percentage = amount bet across all numbers
× 100
House advantage = 100 − win %
payout
F air payout for a win = win %
expected prof it ∨ loss
% return on amount bet = bet amount
House advantage = − % return
STA1000S 1
, Basics
Roulette uses the numbers 0 → 37
but 0 is 'dead'
There are 37 options
when using probabilities, there are 36 options
Work Unit 2: Set Theory, Probability Axioms &
Theorems
Basics
Sample Space (S)
Universal set
All objects under consideration
Subset ( ⊂ or ⊃)
One set is contained in another set
Empty Set (Ø or {})
Has no members
If the intersection of 2 sets is an empty set:
the sets are mutually exclusive / disjoint
Intersection (∩)
and
The intersection of any 2 sets: the set that contains exactly those elements
which belong to both sets
STA1000S 2
