chapter 5 probability

random process

generates outcomes determined purely by chance

trial

one repetition of a random process

probability

chance process is a number between 0-1 that describes the proportion of times the outcome would occur in series of repetitions

law of large numbers

observing more & more repetitions of any chance process the proportion of times that a specific outcome occurs approaches its probability

probability model

description of some chance process that consists of two parts

• all possible outcomes

• probability for each outcome

sample space

list of all possible outcomes

mutually exclusive events

events a & b are mutually exclusive if it is impossible for the events to occur at the exact same time from single trial — P (A and B) = 0

addition rule

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

complement

A^c — contains exactly the outcomes not in A

intersection

(A & B) — the set of all outcomes in both events

union

(A or B) — set of outcomes in either event

conditional probability

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

• not possible for events to be independent & mutually exclusive

independent events

events A & B are independent if one of them occurring does not change the probability of the other event occurring

tree diagram

shows the sample space of a chance process involving multiple stages

• probability of each outcome is show on corresponding branch

• after first stage the probabilities are conditional

probability of at least one

P (at least one) = 1- P(event never occurs) ^n)

• n = how many don’t

multiplication rule (dependent events)

P (A and B) = P(A) x P (B given A)

multiplication rule (independent events)

P (A & B) = P(A) x P(B)