Deterministic processes 
outcome can be predicted exactly in advance 
Random processes 
outcome is not known exactly (can desc the probability distribution of possible outcomes) 
Probability of event A 
0<=P(A)<=1 
Probability of whole sample space 
P(S)=1, P(A)+P(B)+P(C) = 1 
Event A will almost definitely not occur 
P(A)=0 
Only small chance that event A will occur 
P(A)=0.1 
5050 chance that event A will occur 
P(A)=0.5 
Strong chance that event A will occur 
P(A)=0.9 
Event A will almost definitely occur 
P(A)=1 
Probability successful outcome (S) 
P(S) = r/n ; r: num of successful outcomes, n: total num of equally likely outcomes 
Permutations 
Order is taken into account 
Combinations 
Order is not important 
Permutation with repetition 
n^r 
Permutation without repetition 
n!/(nr)! 
Combination with repetition 
(r+n1)!/r!(n1)! 
Combination without repetition 
n!/(nr)! 

n: number of things to choose from ; r: them are chosen 
Probability events A and B both occur 
P(A∩B) 
Events A and B are mutually exclusive or disjoint cannot occur at the same time 
P{AB}=0, P{A∩B}=0 
Probability events A or B occur 
P(A∪B) 
Conditional probability (event A occurs, given that event B has occured) 
P(AB) 
Independent (event A does not change the probability of event B) 
P{AB} = P(A) 
Complement (event that not occuring) 
P(A') 
Rule of subtraction (event A will occur) 
P(A) = 1  P(A') 
Rule of multiplication (probability of the intersection of two events) 
P(A∩B) = P(A) x P(BA) 
Rule of addition (either event occurs, not mutually exclusive) 
P(A∪B) = P(A) + P(B)  P(A∩B) 

P(A∪B) = P(A) + P(B)  (P(A) x P(BA)) 
Random variable 
determined by a chance event, outcome of a random experiment, measurable realvalued 
Discrete random variable 
range of X is finite ot countably infinite (values X can take on, not the size of the values) 
Continuous random variable 
range of X is uncountably infinite (that makes a physical measurement) 