Topic 2A Probability Flashcards
What’s the key difference between Frequentist and Bayesian interpretations of probability?
Frequentist: based on frequency of occurrence. Bayesian: based on degree of belief/confidence.
The mathematics of how you calculate probability is _______ of how it’s interpreted.
independent
What is a sample space in probability?
The set of all possible outcomes of an experiment (denoted Ω).
An event is a _______ of the sample space.
subset
Definitions:
A ∩ B: _______
A ∪ B: _______
A̅: _______
A ∩ B: intersection (A and B)
A ∪ B: union (A or B)
A̅: complement (not A)
If A = <10 accidents and B = 5–25 accidents, what is A ∩ B?
5–10 accidents
Formula
Classical probability:
P(A) = (Number of ways A can occur) / (Total outcomes)
P(Ω) = ___
P(∅) = ___
1
0
Match each event type:
Rolling a 3 then a 5 → ______
Coin toss outcomes independent → ______
Drawing 2 cards without replacement → ______
Mutually exclusive
Independent
Dependent
Formula
Complement Rule:
P(A̅) = 1 − P(A)
Formula
Addition Rule (non-mutually exclusive):
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
If A and B are mutually exclusive, P(A ∩ B) = __
0
What’s the difference between permutations and combinations?
Permutations consider order; combinations do not.
Formula Recall
Permutations without repetition:
nPk = n! / (n − k)!
Formula Recall
Combinations without repetition:
nCk = n! / [(n − k)! k!]
Conditional Probability Formula:
P(A|B) = P(A ∩ B) / P(B)
Definition
Mutually exclusive:
Events cannot occur at same time
Definition
Independent:
Event is not affected by previous events
Definition
Dependent:
Event is affected by other events
Formula
P(A ∩ B) = P(A|B) × ____
P(B)
When are two events A and B independent?
When P(A|B) = P(A)
What is formula for P(A ∩ B) when they A and B are independent?
P(A) × P(B)
Formula
Law of Total Probability:
P(B) = Σ P(B|Ai) × P(Ai)
(where {Ai} is a partition of the sample space)
Formula
Bayes’ Theorem:
P(A|B) = [P(B|A) × P(A)] / P(B)
What are prior and posterior probabilities in Bayes’ Law?
Prior = P(A), Posterior = P(A|B)
Formula
Chain Rule:
P(A ∩ B ∩ C) = P(A|B ∩ C) × P(B|C) × P(C)
Which of the following is Bayes’ Theorem?
A. P(A ∩ B) = P(A) + P(B)
B. P(A|B) = [P(B|A) × P(A)] / P(B)
C. P(A|B) = P(B) / P(A)
B
In the total probability law, the events {Ai} must form a _______ of the sample space.
partition
Formula
Permutation with repetition:
∏ᴺᵢ₌₁ mᵢ
N events, each with mi
options then the total number of outcomes
