Exam 2 notes

# Exam 2 notes - Chapter 7 Probability P(A)= Probability...

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Chapter 7: Probability P(A)= Probability event A occurs P(A c )= represents the "probability that the complement of event A occurs" Ex. 3 political party affiliations: Republican, Democrat, and Independent P(A) = probability of being an Independent, P(Independent) P(A c ) = of "not being an Independent", P(Republican or Democrat). Two conditions for Valid Probabilities 1.) each probability between 0 & 1 (must be between 0<= P <= 1) 2.) probability for all possible outcomes of a random circumstance is equal to 1 (total over all events must =1) General Probability Rules Rule 1 : probability of an impossible event is zero; probability of a certain event is one. Therefore, for any event A, the range of possible probabilities is: 0 = P(A) = 1 Rule 2: P(S) = 1 *S =sample space of all possibilities T he sum of all the probabilities for all possible events is equal to one . Ex. (referring to political parties) P(R)+ P(D) +P(I) = 1 Rule 3: P(A c ) = 1 - P(A). It follows then that P(A) = 1 - P(A c ) Rule 4 (Addition Rule): This is the probability that either one or both a. mutually exclusive - that is A & B have no outcomes in common - then P(A or B) = P(A) + P(B) b. NOT mutually exclusive , then P(A or B) = P(A) + P(B) - P(A and B) Rule 5 (Multiplication Rule): This is the probability that both events occur a. P(A and B) = P(A)*P(B|A) or P(B)*P(A|B) Note: | This symbols means "conditional" or "given". Ex. P(A|B) means the probability that event A occurs given event B has occurred. b. If A and B are independent - neither event influences or affects the probability that the other event occurs – then P(A and B) = P(A)*P(B). This particular rule extends to more than two independent events. Ex. P(A and B and C) = P(A)*P(B)*P(C) Rule 6 (Conditional Probability): P(A|B) = or P(B|A) = Personal (Subjective ) probability: degree at which a given individual believes that the event will happen ex. "What is the probability that you will leave school before you graduate?" Relative frequency probability: the proportion of times the outcome will occur over the long run ex. 1000 students majoring in humanities 660 were female. 66% (660/1000) chance a humanities major being female Sample space: collection of unique, non-overlapping possible outcomes of a random circumstance Simple Event: one outcome in the sample space (possible outcome of a random circumstance) Event: collection of one or more simple events in the sample space. Complement: 2 events that do not contain any of the same simple events and together they cover entire sample space (A

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## This note was uploaded on 03/29/2008 for the course STAT 200 taught by Professor Barroso,joaor during the Spring '08 term at Penn State.

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Exam 2 notes - Chapter 7 Probability P(A)= Probability...

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