Chapter 5: Probability

random process

generates outcomes purely by chance

probability

 a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of trials

law of large numbers

 if we observe more and more trials of any random process, the proportion of times that a specific outcome occurs approaches its probability

simulation

 process that imitates a random process in such a way that simulated outcomes are consistent with real-world outcomes. 

simulation process

describe, perform, use results

probability model

 a description of some random process that consists of two parts: a list of all possible outcomes and the probability for each outcome

sample space

 list of all possible outcomes

event

any collection of outcomes from some random process

complement rule

 P(A^C)= 1 - P(A), where A^C is the complement of event A

complement

the event that a certain outcome does not occur

mutually exclusive (disjoint)

no outcomes in common and so can never occur together - that is, if P(A and B) = 0

addition rule for mutually exclusive events

P(A or B) = P(A) + P(B)

general addition rule

 P(A or B) = P(A) + P(B) - P(A and B)

intersection of A and B

“A and B”, consists of outcomes that are common to both events, notated as A ∩ B

union of A and B

“A or B”, consists of outcomes that are in either event or both, notated as A ∪ B

conditional probability

 probability that one event happens given that another event is known to have happened

conditional probability of A given B

notated as A | B, solved with this equation

independent events

 if knowing whether or not one event has occurred does not change the probability that the other event will happen

A and B are independent if

P(A|B) = P(A|B^C) = P(A) OR P(B|A) = P(B|A^C) = P(B)

general multiplication rule

 P(A and B) = P(A ∩ B) = P(A) x P(B|A)

all probabilities after the ____ stage on a tree diagram are conditional

first

if A and B are independent, the probability that A and B both occur

P(A and B) = P(A ∩ B) = P(A) x P(B)