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