Chapter 5 - Randomness, Probability, and Simulation Flashcards
law of large numbers
if we observe more and more repetitions of any chance process, the proportion of times that a specific outcome occurs approaches a single value
describe chance behavior
unpredictable in the short run but has a regular and predictable pattern in the long run
probability
any outcome of a chance process is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions
law of averages
myth that probability tells us random behavior evens out in the long run. future outcomes are not affected by past behavior
simulation
imitation of chance behavior, based on a model that accurately reflects the situation
performing a simulation
state
plan
do
conclude
sample space s
set of all possible outcomes
probability model
description of some chance process that consists of two parts: sample space s & a probability for each outcome
event
any collection of outcomes from a chance process.
usually designated by capital letters
complement
“not A”
two events A and B are ____ if they have no outcomes in common and so can never occur together
mutually exclusive (disjoint)
basic probability rules
-for any event A, P must be equal to 0 or 1 or i between
-if s is the sample space, P(S) = 1
-in case of equally likely outcomes use
P(A)= # outcomes corresponding to A / total # of outcomes in sample space
-Complement rule = P(A^c) = 1 - P(A)
-addition rule for mutually exclusive events: If A and B are mutually exclusive, P(A or B) = P(A) + P(B)_
P(A or B) = P(A) + P(B)
addition rule for mutually exclusive events
P(A or B) = P(A) + P(B) - P(A and B)
General addition rule for two events
event A or B
A union B
