Chapter 1 - Fundamentals Of Probability Flashcards
What is an event?
Events are subsets of a sample space. An event is a set of outcomes and may contain one or more of the values in the sample space, or it may contain no elements.
What is a mutually exclusive event?
An event that can happen but not if another event happens instead. Mutually exclusive events cannot occur together.
Mutually exclusive events cannot be independent.
What is an independent event?
An event that does not have its probability of occuring affected by whether or not another event occurs.
Two events are independent if the probability that both events occur is the product of the probability of each event.
The formula of an independent event is: Pra(A[intersection]B) = Pra(A) x Pr(B).
What is the definition of a conditional probability?
A conditional probability is a probability that is dependent on an outcome in a different set. E.g. Pr(A[intersectionB|C ) is the probability of an outcome occuring in both A and B, given that an outcome in C occurs.
How is conditional probability calculated?
Pr(A|B = Pr(A[intersection]B % Pr(B)
What is the difference between conditional and unconditional probabilities?
Unconditional probability refers to a probability that is unaffected by previous or future events.
Conditional probability is the probability of an event that would affected by another event.
What is Bayes’ rule? Define it
Bayes’ rule provides a method to construct conditional probabilities using other probability measures.
The formal statement of Bayes’ rule is:
Pr(B|A) = Pr(A|B) Pr(B) / Pr(A).
This approach uses the unconditional probabilities of A and B, as well as information about the conditional probability of A given B, to compute the probability of B given A.
What is an event space?
An event space consists of all combinations of outcomes to which probabilities can be assigned. (note - the event space is an abstract concept and separate from any specific application).
Event spaces contain all sets that can be assigned a probability - even those that have a definite probability of 0 (impossible events).
What is a discrete probability space?
A discrete probability space is a when an event space has a finite number of outcomes.
Give a simple interpretation of probability
Probability is the frequency with which an event would occur if a set of independent experiments was run.
What does the intersection (upside down U) operator show in sets?
The intersection operator indicates a set of outcomes that appear in multiple sets.
What does the union (looks like a U) operator show in sets?
The union operator indicates that the set contains all outcomes in either set or both.
What does the complement (Raised C like a little c, like a to the power of) indiciate in sets?
The complement indicator refers to the set of all outcomes that are not present in a particular set.
What are the three axioms of probability?
Any event A in the event space F has Pr(A) >/= 0.
2. The probability of all events in Ω is one and thus Pr(Ω) = 1.
3. If the events A1 and A2 are mutually exclusive, then Pr(A1UA2) = Pr(A1) + Pr(A2). This holds for any number n of mutually exclusive events, so that Pr(A1UA2…UAn) =a
n i = 1Pr(Ai).5
