Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
54 Cards in this Set
- Front
- Back
What is the rare event rule for inferential statistics?
|
If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct.
|
|
Probability values are expressed as values between:
|
0 and 1
|
|
Any collection of results or outcomes of a procedure.
|
An event
|
|
An outcome or an event that cannot be further broken down into simpler components.
|
A simple event
|
|
The sample space for a procedure consists of:
|
all possible simple events; all outcomes that cannot be broken down any further.
|
|
In the notation for probabilities:
P denotes: A, B, and C denote: P(A) denotes: |
P denotes: a probability
A, B, and C denote: specific events P(A) denotes: the probability of event A occuring |
|
What are the three different approaches to finding the probability of an event?
|
Relative Frequency Approach
Classical Approach Subjective Probability |
|
How is the Relative Frequency approach conducted?
|
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. |
|
How is Classical approach conducted?
|
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 |
|
When calculating the probability of an event using the Classical approach, what must always be verified?
|
You must always verify that the outcomes are equally likely.
|
|
The Classical approach requires:
|
equally likely outcomes
|
|
If the outcomes are not equally likely, we must use:
|
the Relative frequency approximation or we must rely on our knowledge of the circumstances to make an educated guess.
|
|
How is the probability of an event found using Subjective probabilities?
|
P(A) is estimated by using knowledge of the relevant circumstances.
|
|
When finding probabilities with the relative frequency approach, we obtain:
|
an approximation instead of an exact value.
|
|
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:
|
get closer to the actual probability.
This property is stated as a theorem commonly referred to as the law of large numbers. |
|
The complement of event A is denoted:
|
A̅
|
|
The complement of event A consists of:
|
all outcomes in which event A does not occur.
|
|
The actual odds in favor of event A occurring are the ratio:
|
P(A) : P(A̅)
|
|
The actual odds against event A occurring are the ratio:
|
P(A̅) : P(A)
|
|
odds are usually expressed in the form:
|
a:b (or a to b), where a and b are integers having no common factors.
|
|
The odds in favor of event A occurring is the __________ of the actual odds against that event.
|
reciprocal
|
|
If the odds in favor of A are a:b, then the odds against A are:
|
b:a
|
|
The payoff odds against event A occurring are:
|
the ratio of net profit (if you win) to the amount bet.
|
|
payoff odds against event A =
|
net profit : amount bet
|
|
payoff odds of event A occurring =
|
amount bet : net profit
|
|
Any event combining two or more simple events.
|
A compound event
|
|
What is the formal addition rule?
|
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. |
|
What is the intuitive addition rule?
|
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.
|
|
Events A and B are disjoint (or mutually exclusive) if:
|
they cannot occur at the same time. (That is, disjoint events do not overlap).
|
|
If A and B are disjoint, P(A and B) =
|
zero
|
|
What is the addition rule for disjoint events?
|
P(A or A̅) = P(A) + P(A̅) = 1
|
|
In the rule for complementary events, P(A̅) =
|
1 - P(A)
|
|
In the rule for complementary events, P(A) =
|
1 - P(A̅)
|
|
P(A and B) =
|
P( event A occurs in a first trial and event B occurs in a second trial)
|
|
Two events, A and B are independent if:
|
the occurrence of one does not affect the probability of the occurrence of the other.
|
|
If A and B are not independent, they are said to be:
|
dependent
|
|
Two events are dependent if:
|
the occurrence of one of them affects the probability of the occurrence of the other.
|
|
B|A is read:
|
"B given A" or "event B occurring after event A has already occurred."
|
|
What is the formal multiplication rule?
|
P(A and B) = P(A) • P(B|A)
|
|
If A and B are independent events, then P(B|A) is the same as:
|
P(B)
|
|
What is the intuitive multiplication rule?
|
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.
|
|
What are the steps for applying the multiplication rule P(A and B)?
|
- 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) |
|
What do you need to make sure to do when calculating P(A and B) = P(A) • P(B|A)?
|
Be sure to find the probability of event B by assuming that event A has already occurred.
|
|
What is the formula for finding at least one of an event?
|
P( at least one) = 1 - P(none)
|
|
What is the procedure for finding the probability of at least one of some event?
|
1) calculate the probability of none.
2) subtract this from 1. |
|
A probability that is obtained with the additional information that some other event has already occurred.
|
a conditional probability
|
|
What is the formula for conditional probability?
|
P(B|A) = P( A and B)/ P(A)
|
|
What is the fundamental counting rule?
|
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.
|
|
0! (read zero factorial) =
|
1
|
|
The factorial symbol represents:
|
The product of decreasing positive whole numbers.
|
|
What is the formula for permutations?
|
(sub n)Pᵣ = n!/(n - r)!
|
|
Does order matter in permutations or combinations?
|
order matters in permutations but not in combinations.
|
|
What is the formula for permutations if there are some items that are identical to others?
|
n! / n₁!n₂!...n(sub k)!
|
|
What is the formula for combinations?
|
(sub n)Cᵣ = n!/(n - r)!r!
|