Probaility
a chance process of an outcome is number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions
Law of large Numbers
says that the proportion of times that a particular outcome occurs in many repetitions will approach a single number
Sample space, S
The set of all possible outcomes of a chance process
Probability Model
A description of some chance process that consists of two parts: a sample space S and a probability for each outcome.
Event
any collection of outcomes from some chance process ( That is, an event is a subset of the sample space. Events are usually designated by capital letters, like A, B, C, and so on)
Mutually exclusive (disjoint)
if two events A and B have no outcomes in common and so can never occur together- that is, if P(A and B) = 0. If A and B are disjoint, P(A or B) = P(A) + P(B)
Union
the event "A or B", notation: AuB
Intersection
the event of "A and B", notation: AnB
Complement Rule
P(A^c) = 1 - P(A)
General Addition Rule
If A and B are any two events resulting from some chance process, then P(A or B) = P(A) + P(B) - P(A and B)
Conditional Probability
the probability that one event happens given that another event is already known to have happened, denoted P(B|A)
General Multiplication Rule
the probability that events A and B both occur can be found by P(A and B) = P(AnB) = P(A) * P(B|A), where P(B|A) is the conditional probability that event B occurs given that event A has already occurred
Independent Events
If the occurrence of one event A, does not affect the probability of the other event, B, will happen (in other words, events A and B are independent if P(A|B) = P(A) and P(B|A) =P(B))
Multiplication Rule for Independent Events
if A and B are independent events, then the probability that A and B both occur is P(AnB) = P(A) * P(B)