test 2
Mutually exclusive
"at least earning a silver medal" (outcomes of gold and silver) "at most earning a silver medal" (outcomes of silver, bronze, no medal) -These two events are exhaustive -The occurrence of one event precludes the occurence of the other.
empirical probability
relative frequency of an event is used to calculate what time
the probability that anthony is on time for work is 0.90. the probability that anthony takes the train to work is 0.80. given that anthony takes the train to work, the probability that he is on is 0.95 the probability that anthony is on time for work and takes the train is
0.76 p( on time u train)= p(on timeI Train)=0.95 x 0.80=0.76
empirical probability
p(a)=The number of outcomes in A / THE NUMBER OF OUTCOMES IN s
a festival has become so popular that it must limit the number of tickets it issues. people who hope to attend the festival send in request for tickets, and requests are filled by random selection. only 21% of the ticket request are fulfilled. the odds that a random applicant does not receive a ticket are
3.76 to 1 (1-0.21)/0.21 =3.76
a probability based on logical analysis rather than on observation or personal judgement is best referred to as an
priori probability
Sample space
Denoted by S, of an experiment records all possible outcomes the experiment. ex: S= (A, B, C, D, F) for grades
using the multiplication rule, the probability that event A and event B both occur is computed by multiplying the conditional probaility of event A given event B by the probability of
Event b
function that assigns numberical values to the outcomes of a randome xperiement
random variable
Experiment
Trial that results in any one of several possible outcomes.
the untion of two events a and b denoted A u B contains
all outcomes in A or B
the complement of event a within the sample space S contains
all outcomes in S that are not in A
if an experiment is selecting a card from a deck of cards, the the sample space is
all the cards in the deck
Example of empirical probability
based on the past data, a manger believes there is a 70% chase of retaining an emplee for at least one year
mutually exclusive and collectively exhaustive events
contain all outcomes in an experiment and do not share common outcomes
Events that cannot both occur on the same trial of an experiment are mutually
exclusive events
events that include all outcomes in the sample space are known as
exhaustive events
a trail, or process, that produces several possible outcomes is referred to as an
experiment
multiplication rule
finding the probability that two events, A and B both occur. P(A B). aka; joint probability- the occurrence of two events, A and B.
Exhaustive
include all outcomes in the sample space. They exhaust the entire sample space. This contrasts with the earlier grade-distribution example, where the events of getting grades A and B are not exhaustive because they do not include many feasible grades in the sample space. P and F are exhaustive, Pass or Fail.
the probability that a customer will purchase a product is 0.15. The probability that a customer is a male 0.5. the probabiliity that a customer is a male and will purchase a product is 0.075. the events purchasing a product and being a male are
independent
conditional probability
is the probability of an event given that another event has already occurred
Probability
numberical value that measures the lielihood that is uncertain event occurs. This value is between zero and one, where a calue of zero indicates impossible events and a value of one definite events.
how many outcomes of an experiment constitutes a simple event
one
the sum of the probabilities of a list of mutually exclusive and exhaustive events is
one
a probability based on personal judgement rather than on observation or logical analysis is best referred to as an
subjective probability
Event
subset of the sample space
combination formula
the number of ways to choose x objects from a total of n objects where the order in the x objects are listed does not matter
The permutation formula
the number of ways to choose x objects from a total of n objects, where the order in which the x objects is listed does matter,
if two events are independent then the probability that both events occur equals
the product of the individual probabilities
contingency tables and probabilities
when organizing qualitative data, it is often useful to construct a frequency distribution. A frequency distribution is a useful tool when we want to sort one variable at a time. However, in many instances we want to examine or compare two qualitative variables. On these occasions, a contingency table proves very useful. Contingency tables are widely used in a marketing and biomedical research, as well as in the social sciences.
probability values range from
zero to one
