L04 (Basic Probability Concepts and Discrete Probability Distributions) - AQM

simple events

only has one outcome

simple probability

probability of simple event 

compound event

combination of multiple simple events

compound probability

probability of compound event

mutually exclusive events

events that cannot occur at the same time

special addition rule

when the two events are mutually exclusive and don’t overlap, add up two probabilities P(A or B) = P(A) + P(B)

collectively exhaustive events

 a set of events where at least one of events in guaranteed to occur, covering all possible outcomes / the entire sample space

complement event

two mutually exclusive and collectively exhaustive outcomes of a random experiment, meaning that only one of the two can occur, and together they cover all possible outcomes

non-mutually exclusive

 events that can occur at the same time

general addition rule

when the two events are not mutually exclusive and overlap P(A or B) = P(A) + P(B) - P(A and B)

conditional probability

the probabilities of one event, given ( | ) that another event has occurred

binomial distribution

models the probability of a specific number of “successes” in a fixed number of independent trials, where each trial has only two possible outcomes and the probability of success is constant for every trial