probability (chapter 5)

empirical vs classical probabilities

empirical: determined by making observations and gathering data; experiments

classical: determined by reasoning mathematically

law of large numbers

as the number of repetitions of a probability experiment increase, the proportion with which a certain outcome is observed gets closer to the probability of the outcome; empirical probability with begin to match up with classical probability

sample space (S)

collection of all possible outcomes; an event is any collection of outcomes from a probability experiment

rules of probability

approximating probability using empirical method

computing probability using the classical method

disjoint

events that cannot happen at the same time, or have no outcomes in a common

addition rule for disjoint events

general additional rule for non-disjoint events

subtract off double counting

complement of an event

denoted E^C is all outcomes in the sample space S that are not outcomes in the event E

ex: 1 - some number/total things

multiplication rule for independent events

or probability vs and probability

or implies addition; and implies multiplication