Topic 2 - Probability Theory Flashcards
(14 cards)
1
Q
What does probability tell us
A
- The likelihood of an event to occur
2
Q
What is S in terms of probability
A
- The sample space of all possible outcomes
3
Q
How are events related to the sample space
A
- Events are an subset A of the sample space
4
Q
What is the probability for the empty set
A
- An impossible event so 0
5
Q
What are the set of operators for probability
A
- A u B union
- A n B intersection
- A bar opposite of A
6
Q
What are the distributive laws in probability
A
- An(BuC) = (AnB)u(AnC)
- Au(BnC) = (AuB)n(AuC)
7
Q
What are the 3 probability Axioms
A
- P(A) >= 0
- P(S) = 1
- If events are mutually exclusive the union of disjoint events is the sum of the probabilites of the events
8
Q
What are the 4 properties we can derive from the Axioms
A
- P(empty set) = 0
- 1 >= P(A) >= 0
- P(not A) = 1 - P(A)
- P(AuB) = P(A) + P(B) - P(AnB)
9
Q
What is conditional probability
A
- The probability of an event depending on whether another event has occured
10
Q
What is the formula for conditional probability
A
- P(A|B) = P(AnB) / P(B)
- P(B|A) = P(BnA) / P(A)
11
Q
How does commutivity work with probability
A
- P(AnB) = P(BnA)
- P(A|B) != P(B|A)
12
Q
What conditions confirm whether two events are independent
A
- P(A|B) = P(A)
- P(B|A) = P(B)
- P(AnB) = P(A) * P(B)
13
Q
What is the law of total probability
A
P(A) = sum P(A|Bi) * P(Bi)
14
Q
Define Bayes Rule
A
look up
