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