Studied by 9 peopleand
both events must happen, multiply, ∩
or
at least 1 event must happen, add, ∪
1 - p(event)
p(event not occurring)
disjoint/mutually exclusive
events with no outcomes in common (both can’t happen at the same time)
sampling with replacement
putting something back after you pick it (probability stays the same)
sampling without replacement
don’t put things back after choosing them (probability changes)
1 - p(none)
p(at least one)
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 predicted probability
probability of 1
event always happens
probability of 0
event never happens
myth of short-run regularity
randomness is predictable in long run, NOT short run
myth of law of averages
future outcomes are not affected by past behavior
state question of interest
describe how to use a chance device to imitate one repetition of process
perform many repetitions
use results to answer question
explaining a simulation
p(a|b)= p(a and b) / p(b)
conditional probability formula
p(a|b) = p(a)
checking for independence
Note
Flashcard