Unit 4 - Probability and Discrete Distributions Flashcards
Define random
if individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions
Define probability
the proportion of times the outcome would occur in an infinitely long series of trialss
What its the 2 components of the probability model?
- list of possible outcomes
- a probability for each outcome
Define sample space (S)
set of all possible outcomes
Define event
any subset of outcomes in the sample space
How do you calculate the probability of an event A?
P9A) = # of outcomes in A/ # of outcomes in S
Define intersection
all outcomes contained in both A and B (also includes the probability that both events occur simultaneously)
What is the symbol of intersection of events?
A ∩ B
Define union
consists of all outcomes that are contained in at least one of the events A OR B (included the probability that they both occur)
What is the symbol of union of events?
A ∪ B
What is a way of calculating the probability of the union of two events?
P(A∪B) = P(A) + P(B) - P(A∩B)
When are two events are said to be mutually exclusive/disjoint?
if they have no outcomes in common
A ∩ B = Ø
What does Ø mean?
empty set, set containing no outcomes
When are 2 events said to be mutually exclusive?
if and only if P(A and B) = 0
What is the equation of calculating when 2 events are mutually exclusive?
P(A∪B) = P(A) + P(B)
Define exhaustive
if they together contain all the outcomes in S
What is the complement of an event A?
the event consisting of all outcomes in the sample space which are not contained in A
What is the symbol of complements?
A^c
What is the probability of complements?
P(A^c) = 1 - P(A)
When are 2 events said to be complements?
if they are both mutually exclusive and exhaustive of the sample space
Define conditional probability
the probability that the event A occurs, given that an event B has occurred
What is the symbol of conditional probability
P(A|B)
How do you calculate P(A|B)?
P(A|B) = P(A∩B)/P(B)
What its the definition of conditional probability (probability of intersections)?
P(A∩B) = P(A)P(B|A) = P(B)P(A|B)
By the definition of conditional probability, what is the the probability of P(C|A∩B)?
P(C|A∩B) = P(A∩B∩C)/P(A∩B)
What is the equation if two events A and B are said to be independent?
P(B|A) = P(B)
or
P(A|B) = P(A)
A and B are independent if and only if what?
P(A∩B) = P(A)P(B)
3 steps to find the probability of an event
1) list all outcomes contained in the event
2) find the probability of each of these outcomes
3) add these probabilities
