probability basics Flashcards
(16 cards)
sample space
set of all possible outcomes
event
a subset of the sample space
event space
a set of events or subsets that satisfy certain properties
axiom 1: probability of an event is more than….
or equal to 0
axiom 2: the probability of the sample space =
1
axiom 3: if events are mutually exclusive the probability of the union of all the events is the same as…
the sum of the probabilities of each individual event
complement rule
P(A’) = 1 - P(A)
probability of the union of two events rule
P(A u B) = P(A) + P(B) - P(A n B)
bounds on probabilities rule
P(A u B) < P(A) + P(B)
conditional probability definition
the probability of an event occurring given that another event has already occurred
conditional probability notation [A given B]
P(A I B)
conditional probability rule
P(A I B) = P(A n B) / P(B)
what does it mean if two events are independent?
they do not have an effect on one another
rule 1 for independent events:
P(A n B) =
P(A)P(B)
rule 2 for independent events:
P(A I B) =
P(A)
bayes rule
P(A I B) = P(B I A) P(A) / P(B)
