# 4.1-4.3

 The flashcards below were created by user khonka on FreezingBlue Flashcards. Probability for equally likely outcomes (f/N rule) to measure probability or to measure the possible outcomes (measuring uncertainty)Suppose an experiment has N possible outcomes, all equally likely. An event that can occur in f ways has probabilyt of f/N occurring:Probability of an event = f <-- number of ways event can occurN <-- total number of possible outcomesexperiment: an action whose outcome cannot be predicted with curtaintyevent: some specified result that may or may not occur when an experiment is performedex. f =7534N 75617 = 0.100Interpretation 10.0% of familied makte between so and so Frequentist interpretation of probability( the meaning of probability) (when outcomes are equally likely probabilities are nothing more than percentage (relative frequency))When number of tosses is small the probability is flactuates a lot. When number of tosses is largethe probability stabelizes (50/50)Interpretation of probability: a probability near 0 (ex. 0.2) indicates that the event in question is very unlikely to occur when the experiment is performed.When a probability near 1 (100%)(0.8) suggests that the event is quite likely to occur. Probability model although the frequentist interpretation is helpful for understanding the meaning of probability, it cannot be used as a definition of probability. One common way to define probabilities is to specify a probability model - a mathematical description of the experiment based on certain primary aspects and assumptions.Equal-likelihood model: is a axample of probability model. Its primary aspect and assumption are that all possible outcomes are equally likely to occur. Basic properties of probabilities Property 1: The probability of an event is always between 0 and 1, inclusive.Property 2: The probability of an event that cannot occur is 0. ( Such an event is called impossible event)Property 3: The probability of an event that must occur is 1. ( such event called certain event) ex. numbers 5 and -0.23 could not possibly be probabilities. P(E) - probability of event Event and Sample space Event (E) - a collection of outcomes for the experiment, that is, any subset of the sample space. Sample space (S)- the collection of all possible outcomes for an experimentSpecified event occurs - if that event contains the card selected. Ex. if the card selected turns out to be the king of spades, the second and fourth event occur, whereas the first and third events do not. Van diagrams are one of the best ways to portray events and relationships among events visually.S - rectangleE -disks, circles inside the rectangle Complement of E everything ot side of E "not E"The event "E does not occur" A & B A intersection B or A B, A and BThe event " both A and B occur"All outcomes common to event A and event B. A or B The event "either A or B or both"A union B, A Bevent A or B consists of all outcomes either in event A or in Event B or both. equivalently, that "at least one of event A and B occurs" Mutually Excllusive Events two or more events are mutually exclusive events if not two of them have outcomes in commonsimbol Fee intersection is emptyempty set no elements in it 4.2 Homework problem less than 7% - means 7 not includedAt least 8% - 8 and more write event in parenthesisC' - complement of C Probability Notation if E is an event, the P(E) represent the probability that event E occurs. Read as " the probability of E" Special addition rule applied only to mutually exclusive eventsP(A or B)= P(A) + P(B) The complement rule P(E)+P(not E)= 1 orP(E) = 1-P(not E) General Addition Rule used for any event that is not mutually exclusiveP(A or B) = P(A) + P(B) - P(A&B) without using Genral addition rule can be done by fN rule The general addition rule is consistent with the special addition rule - if two events are mutually exclusive, both rules yeild the same resultGeneral addition rule for more than 2 eventsex. for 3 eventsP(A or B or C) = P(A) + P(B) + P(C) -P(A&B) - P(A&C) - P(B&C) + P(A&B&C) P(S) P(S)= 1 probability of a sample set means all events 36/36=1 Authorkhonka ID42945 Card Set4.1-4.3 DescriptionProbability concept Updated2010-10-22T16:59:59Z Show Answers