chapter 5
is FAKE
"Law of Averages"
model based (theoretical prob)
#outcomes in a/total outcomes
independent
Events A and B are _______ whenever P(B|A) = P(B). this means knowing event a has occurred has NO impact on the probability of event B
long-run relative frequencies or on equally likely events.
Although personal probabilities may be based on experience, they are not based either on _________
independent vs. disjoint
For all practical purposes, disjoint events cannot be independent. Don't make the mistake of treating disjoint events as if they were independent and applying the Multiplication Rule for independent events.
or trial, outcome.
For any random phenomenon, each attempt, or ________, generates an ________.
0 and 1
Individual probabilities must be between_________
S or sometimes Ω.
We denote the sample space ____ or sometimes ____.
event
We use the more general term ______ to refer to outcomes or combinations of outcomes.
P(A)=1-P(A^C)
compliment rule
P(A or B)=P(A)+P(B)-P(A and B)
general addition rule
P(A and B)=P(A)*P(BIA)
general multiplication rule
P(A and B)=P(A)*P(B) INDEPEDENT only
multiplication rule
general multiplication rule calculates the probability that both of two events occurs. It does not require that the events be independent. P(A and B)=P(A)*P(BIA)
probability rule #7
probability assignment rule The probability of the set of all possible outcomes must be 1 P(S)=1 s reps the set of all possible outcomes called the sample space
probability rule 2
multiplication rule For two independent events A and B, the probability that both A and B occur is the product of the probabilities of the two events. P(a and b)= P(A)*P(B) A and B are independent
probability rule 4
The Law of Large Numbers (LLN)
states that if the events are independent, then as the number of trials increases, the long-run relative frequency of an event gets closer and closer to a single value.
be aware of probabilities that do NOT add up to 1 do NOT add probabilities of events if they are not DISJOINT Do NOT multiply props of events when they are not independent Do NOT confuse disjoint with independent
what can go wrong?
What percentage of adults do not conduct their banking online? 100% - 30% = 70% What type of probability is the 25% mentioned above? Marginal What is the probability that an individual who is under the age of 50 conducts banking online? 0.25 / 0.40 = 0.625 Are Banking online and Age independent? No. P(banking online | under 50) = 0.625, which is not equal to P(banking online) = 0.30.
A national survey indicated that 30% of adults conduct their banking online. It also found that 40% are under the age of 50, and that 25% are under the age of 50 and conduct their banking online. What percentage of adults do not conduct their banking online? What type of probability is the 25% mentioned above? Construct a contingency table showing joint and marginal probabilities. What is the probability that an individual who is under the age of 50 conducts banking online? Are Banking online and Age independent?
conditional probability.
A probability that takes into account a given condition is called a __________.
, or personal probability
A subjective, or_______ expresses your uncertainty about the outcome.
joint probabilities multiplication rule
At the end of each branch,-------- can be calculated by applying the ------- for independent events.
conditional distribution
Each row or column shows a _________ given one event.
Empirical probability
Empirical probability is based on repeatedly observing the event's outcome.
probability tree or tree diagram
Given the probabilities of various states of nature, we can use a picture called a _________to help think through the decision-making process.
P(B|A) "the probability of B given A."
In general, when we want the probability of an event from a conditional distribution, we write ______ and pronounce it __________
long-run relative frequency.
Probability is __________
sample space
S reps
P(a)=#outcomes in A/total # of outcomes
The (theoretical) probability of event A can be computed with the following equation:
doesn't exist.
The Law of Averages _____
probability .
The _________ of an event is its long-run relative frequency.
sample space
The _____________ is the collection of all possible outcomes.
1
The sum of probabilities assigned to all outcomes must be _____
reverse the conditioning: Baye's Rule
When you need to find reverse conditional probabilities, we recommend drawing a tree and finding the appropriate probabilities by using the definition of conditional probability (see text).
random phenomena
With ___________ we can't predict the individual outcomes, but we can hope to understand characteristics of their long-run behavior.
Marginal probability
________ depends only on totals found in the margins of the table
Joint probabilities
___________ give the probability of two events occurring together.
Independence
___________ means that the outcome of one trial doesn't influence or change the outcome of another.
P(A orB)=P(A)+P(B) DISJOINT
addition rule
P(BIA)=P(Aand B) / P(A)
conditional probability
of the probability of an event occurring is 0 the event can not occur if its 1 it ALWAYs occurs 0 greater or less than P(A) less than or equal to 1
probability Rule 1
Complement rule the prob of an event occurring is 1 minus the prob that it does not occur P(A)=1-P(A^c) where the set of outcomes that are not in the event A is called a "complement of A, denoted as A^c
probability rule #3
addition rule Two events are disjoint (or mutually exclusive) if they have no outcomes in common. The Addition Rule allows us to add the probabilities of disjoint events to get the probability that either event occurs. P(A or B)= P(A)+P(B) A and B disjointed
probability rule #5
the genera addition rule calculates the prob that either of two events occurs. it does not require that events be disjoint. P(A or B)= P(A)+P(B)-P(A and B)
probability rule #6
