Stats 50 Ch. 04

Front 1

What is the rare event rule for inferential statistics?

Back 1

If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct.

Front 2

Probability values are expressed as values between:

Back 2

0 and 1

Front 3

Any collection of results or outcomes of a procedure.

Back 3

An event

Front 4

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

Back 4

A simple event

Front 5

The sample space for a procedure consists of:

Back 5

all possible simple events; all outcomes that cannot be broken down any further.

Front 6

In the notation for probabilities:
P denotes:
A, B, and C denote:
P(A) denotes:

Back 6

P denotes: a probability
A, B, and C denote: specific events
P(A) denotes: the probability of event A occuring

Front 7

What are the three different approaches to finding the probability of an event?

Back 7

Relative Frequency Approach
Classical Approach
Subjective Probability

Front 8

How is the Relative Frequency approach conducted?

Back 8

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

Front 9

How is Classical approach conducted?

Back 9

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:
P(A) = number of ways A can occur / number of different simple events
= s/n

Front 10

When calculating the probability of an event using the Classical approach, what must always be verified?

Back 10

You must always verify that the outcomes are equally likely.

Front 11

The Classical approach requires:

Back 11

equally likely outcomes

Front 12

If the outcomes are not equally likely, we must use:

Back 12

the Relative frequency approximation or we must rely on our knowledge of the circumstances to make an educated guess.

Front 13

How is the probability of an event found using Subjective probabilities?

Back 13

P(A) is estimated by using knowledge of the relevant circumstances.

Front 14

When finding probabilities with the relative frequency approach, we obtain:

Back 14

an approximation instead of an exact value.

Front 15

When finding probabilities with the relative frequency approach we obtain an approximation instead of an exact value. As the total number of observations increases, the corresponding approximations tend to:

Back 15

get closer to the actual probability.
This property is stated as a theorem commonly referred to as the law of large numbers.

Front 16

The complement of event A is denoted:

Back 16

A̅

Front 17

The complement of event A consists of:

Back 17

all outcomes in which event A does not occur.

Front 18

The actual odds in favor of event A occurring are the ratio:

Back 18

P(A) : P(A̅)

Front 19

The actual odds against event A occurring are the ratio:

Back 19

P(A̅) : P(A)

Front 20

odds are usually expressed in the form:

Back 20

a:b (or a to b), where a and b are integers having no common factors.

Front 21

The odds in favor of event A occurring is the __________ of the actual odds against that event.

Back 21

reciprocal

Front 22

If the odds in favor of A are a:b, then the odds against A are:

Back 22

b:a

Front 23

The payoff odds against event A occurring are:

Back 23

the ratio of net profit (if you win) to the amount bet.

Front 24

payoff odds against event A =

Back 24

net profit : amount bet

Front 25

payoff odds of event A occurring =

Back 25

amount bet : net profit

Front 26

Any event combining two or more simple events.

Back 26

A compound event

Front 27

What is the formal addition rule?

Back 27

P(A or B) = P(A) + P(B) - P(A and B)
Where P(A and B) denotes the probability that A and B both occur at the same time as an outcome in a trial of a procedure.

Front 28

What is the intuitive addition rule?

Back 28

P(A or B) = the sum of the number of ways A can occur and the number of ways B can occur without counting any twice.

Front 29

Events A and B are disjoint (or mutually exclusive) if:

Back 29

they cannot occur at the same time. (That is, disjoint events do not overlap).

Front 30

If A and B are disjoint, P(A and B) =

Back 30

zero

Front 31

What is the addition rule for disjoint events?

Back 31

P(A or A̅) = P(A) + P(A̅) = 1

Front 32

In the rule for complementary events, P(A̅) =

Back 32

1 - P(A)

Front 33

In the rule for complementary events, P(A) =

Back 33

1 - P(A̅)

Front 34

P(A and B) =

Back 34

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

Front 35

Two events, A and B are independent if:

Back 35

the occurrence of one does not affect the probability of the occurrence of the other.

Front 36

If A and B are not independent, they are said to be:

Back 36

dependent

Front 37

Two events are dependent if:

Back 37

the occurrence of one of them affects the probability of the occurrence of the other.

Front 38

B|A is read:

Back 38

"B given A" or "event B occurring after event A has already occurred."

Front 39

What is the formal multiplication rule?

Back 39

P(A and B) = P(A) • P(B|A)

Front 40

If A and B are independent events, then P(B|A) is the same as:

Back 40

P(B)

Front 41

What is the intuitive multiplication rule?

Back 41

Multiply the probability of event A by the probability of event B, but be sure that the probability of event B takes into account the previous occurrence of event A.

Front 42

What are the steps for applying the multiplication rule P(A and B)?

Back 42

- Are A and B independent? If Yes:
P(A and B) = P(A) • P(B)
- If No:
P(A and B) = P(A) • P(B|A)

Front 43

What do you need to make sure to do when calculating P(A and B) = P(A) • P(B|A)?

Back 43

Be sure to find the probability of event B by assuming that event A has already occurred.

Front 44

What is the formula for finding at least one of an event?

Back 44

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

Front 45

What is the procedure for finding the probability of at least one of some event?

Back 45

1) calculate the probability of none.
2) subtract this from 1.

Front 46

A probability that is obtained with the additional information that some other event has already occurred.

Back 46

a conditional probability

Front 47

What is the formula for conditional probability?

Back 47

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

Front 48

What is the fundamental counting rule?

Back 48

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 49

0! (read zero factorial) =

Back 49

1

Front 50

The factorial symbol represents:

Back 50

The product of decreasing positive whole numbers.

Front 51

What is the formula for permutations?

Back 51

(sub n)Pᵣ = n!/(n - r)!

Front 52

Does order matter in permutations or combinations?

Back 52

order matters in permutations but not in combinations.

Front 53

What is the formula for permutations if there are some items that are identical to others?

Back 53

n! / n₁!n₂!...n(sub k)!

Front 54

What is the formula for combinations?

Back 54

(sub n)Cᵣ = n!/(n - r)!r!