Statistics Test 2
What are the two defining properties of probability?
1) The probability of any event A is a value between 0 and 1 2) The sum of the probabilities of any list of mutually exclusive and exhaustive events equals 1
event
A subset of a sample space.
Given two events A and B, each with a positive probability of occurring, the probability that A occurs given that B has occurred (A conditioned on B) is equal to:
P(A/B)=P(A∩B)/P(B)
The probability that B occurs given that A had occurred (B conditioned on A) is equal to:
P(B/A)=P(A∩B)/P(A)
events are _____________ if they do not share any common outcome of an experiment
mutually exclusive
subjective probability
a probability value based on personal and subjective judgement
experiment
a process that to one of several possible outcomes
Given odds FOR event A occurring of "a to b" the probability of A is:
a/a+b
the __________ rule states that the probability that A or B occurs, or that at least one of these events occurs, is equal to the probability that A occurs, plus the probability that B occurs, minus the probability that both A and B occur.
addition
Given odds AGAINST event A occurring of "a to b" the probability of A is b/a+b
b/a+b
______________ are often used in games of chance because they are based on the assumption that all outcomes of an experiment are equally likely.
classical probabilities
deducing probabilities by reasoning about the problem
classical probability
the _________ of event A is the event consisting of all outcomes in the sample space that are not in A.
complement
the __________ rule states that the probability of the complement of an event, is equal to one minus the probability of the event
complement
sample space
contains all the possible outcomes of a probability experiment
Events are considered ____________ if the occurrence of one is related to the probability of the occurrence of the other.
dependent
The experiment must be completed a large number of times for _____________ to be accurate.
empirical probabilities
the _______________ of an event is the observed relative frequency with which an event occurs
empirical probability
exhaustive events
events are those that include all possible outcomes in the sample space
mutually exclusive events
events that cannot happen at the same time
events are __________ if all possible outcomes of an experiment belong to the events.
exhaustive
Two events are ____________ if the occurrence of one event does not affect the probability of the occurrence of the other event.
independent
Two events, A and B are _________ if P(A/B)=P(A) or, equivalently, P(B/A)=P(B). Otherwise, the events are ___________.
independent; dependent
the _________ of two events is the event consisting of all outcomes in A and B.
intersection
The _____________ rule states that the probability that A and B both occur is equal to the probability that A occurs given that B has occurred, times the probability that B occurs.
multiplication;P(A∩B)=P(A/B)P(B) or P(A∩B)=P(B/A)P(A).
conditional probability
the probability that one event happens given that another event is already known to have happened
the _________ of two events is the event consisting of all outcomes in A or B.
union