Stats Test 2

Front 1

Event

Back 1

Any collection of results or outcomes of a procedure

Front 2

Simple event

Back 2

An outcome or an event that cannot be further broken down into simpler components

Front 3

Sample space

Back 3

for procedure consisting of all possible simple events, that is the sample space consists of all outcomes that cannot be broken down any further

Front 4

Relative frequency approximation of probability

Back 4

Conduct or observe a procedure, and count the number of times event a actually occurs. Based on these actual results P(A) is approximated as follows.

Front 5

Classical approach to probability

Back 5

Assume that a given procedure has n different simple events and that each of those simple events has an equal chance of occurring. If event A can occur in s of these n ways then

Front 6

Subjective probabilities

Back 6

Probability of event A is estimated by using knowledge of the relevant circumstances

Front 7

Simulation

Back 7

Process that behaves in the same ways as the procedure itself so that similar results are produced

Front 8

Law of large numbers

Back 8

As a procedure is repeated again and again, the relative frequency probability of an event tends to approach the actual probability

Front 9

Probability limits 0 and 1

Back 9

The probability of an impossible event is 0

The probability of an event that is certain is 1

0≤P(A)≤1

Front 10

Completement of event A

Back 10

Ā consists of all outcomes in which the event A does not occur

Front 11

An event is unlikely when

Back 11

It's probability us very small, such as 0. 05 or less

Front 12

Actual odds against event A

Back 12

P(Ā)

------

P(A)

Expressed in the form a:b (or a to b) (reduce using common factors)

Front 13

Actual odds in favor of event A

Back 13

P(A)

------

P(Ā)

Odds in favor are b:a or b to a

Front 14

Addition rule

Back 14

Finding the probability that are expressed as P(A or B), the probability that either event A occurs or event B occurs (or they both occur) as the single outcome of the procedure.

Key word is or

Front 15

Compound event

Back 15

Any event combining 2 or more simple events

P(A or B)=P(A) + P(B) - P(A and B)

P(A and B) only when both occur at the same time as an outcome in a procedure

Front 16

P(A or B) notation

Back 16

P(in a single trial, event A occurs or Event B occurs or they both occur)

Front 17

Rule for compound events

Back 17

Find the total ways event A can occur and the number of ways B can occur, but find the total in such a way that no outcome is counted more than once

Front 18

Disjoint and mutually exclusive

Back 18

Events A and B are disjoint (mutually exclusive) if they cannot occur at the same time.

A and Ā are disjoint

Front 19

Multiplication rule

Back 19

Used for finding P(A and B), the probability that event A occurs in a first trial and event B occurs in a second trial.

Important to adjust probability of B to reflect the occurrence of event A if it's outcome affects B

Front 20

Multiplication rule notation

Back 20

P(A and B) means event A occurs in a first trial and event B occurs in a second one

P(B|A) means the probability of event B occurring after event A has already occurred

P(A and B) = P(A) • P(B|A)

Front 21

Tree diagrams

Back 21

A picture if the possible outcomes of a procedure, shown as line segments.

Front 22

Probability of at least one

Back 22

Finding the probability that among several trials, we get at least one of some specified event.

At least one is equivalent to "one or more"

The complement of getting at least one item of a particular type is that you get no items of that type

Front 23

At least one notation

Back 23

P(at least one) = 1 - P(none)

Calculate the probability of none and then subtract that result from 1

Front 24

Conditional probability

Back 24

Finding the probability of an event when we have additional information that some other event has already occurred

P(B|A) denotes the conditional probability of event B occurring given that event A has already occurred.

P(B|A) = P(A and B)

---------------

P(A)

Front 25

Confusion of the inverse

Back 25

To incorrectly believe that P(A|B) and P(B|A) are the same, or to incorrectly use one value for the other.

Front 26

Fundamental counting rule

Back 26

For a sequence of two events in which the first event can occur m ways and the second event can occur n ways, the events together can occur a total of m•n ways

Front 27

Factorial symbol

Back 27

Factorial symbol ! denotes the product of decreasing positive whole numbers.

5! = 5•4•3•2•1

By special definition, 0! = 1

Front 28

Permutations

Back 28

Order and rearrangements of the same items counts(ABC is different than (CBA)

There are n different items available (this rule does not apply if some items are identical to others)

We select r of n items( without replacement)

nPr = n!

-------

(n - r)!

Front 29

Combinations rule

Back 29

There are n different b items

We select r of the n items (without replacement)

Rearrangements of the same items are the same(ABC is the same as CBA)

nCr = n!

-----------

(n - r)!r!

Front 30

Probability

Back 30

Likelihood of occurrence of experiment or event over the total possible outcomes

Front 31

Multiplication counting rule

Back 31

Used to find the total number of possibilities from some sequence of events

First event occurs n1 ways, second event occurs n2 ways and so on

n1 • n2 • n3