Probability of events Flashcards
what is probability
long term frequency
what is the law of large numbers?
coin toss is only 50/50 but only clear after many tosses
mutually exclusive
no outcomes in common, heads or tails not both, Pr(AnB) = 0
What is the probability of A when it is mutually exclusive?
P(A) = ways A can happen/total number of events
probability is between
0 and 1
addition rule
if A and B are mutually exclusive, the events of A or B can occur.
Pr(AuB) = P(A) + P(B)
generalised addition rule
when events are not necessarily mutually exclusive
P(AuB) = P(A) + P(B) - P(AnB)
A complement or not A
P(A^c) = 1 - P(A)
product rule
If A and B are independent events, Pr(AnB) = Pr(A) x P(B)
generalised product rule
when A and B are not independent. P(A) does not affect P(B) - marbles are not replaced between draws
Pr(AB) = P(A) x P(B/A) P(AB) = P(B) x P(A/B)
bayes rule
Pr(A/B) = (P(A) x P(B/A))/P(B) = (P(A) x P(B/A)/(P(A) x P(B/A) + P(A^c) x P(B/A^c)
sample space
all possible outcomes (S) eg. {heads or tails}
event
a set of outcomes, a subset of the sample space eg. even numbers on a dice
