What is the addition Rule?
P(A or B) = P(A) + P(B) - P(A and B)
Addition Rule for Mutually Exclusive (or disjoint) Events
P(A or B) = P(A) + P(B) . An alternate
notation is P(A or B) = P(A ∪ B)
Combination:
a way of selecting several things out of a larger group, where order does not matter
Combination Rule
C(n, r) = nCr = n!/r!(n-r)!
Complement Rule
the probability that an event does not occur; 1 – P(A)
Complementary Events
mutually exclusive events whose probabilities sum to 1
Conditional Probability
the probability that an event, B, will occur given that another event, A, has
already occurred
Conditional Probability Rule
P(F|E) =P(F∩E ) / P(E)
Cumulative Relative Frequency
the cumulative proportion or the running total of frequencies
Dependent Events
when the occurrence of one event affects the occurrence of a second event
Empirical Estimate of Probability
(often just written Empirical Probability) an "estimate" that the event will happen based on how often the event occurs after collecting data or running an experiment (in a large number of trials). It is based specifically on direct observations or experiences.
Equally Likely Outcomes
outcomes that occur with the same probability; i.e., landing on heads or tails on a fair coin toss are equally likely outcomes
Event
a subset of a sample space
Expected Value
the long-run average result of a numerical random process
Experimental Estimate of Probability
the probability of an event occurring when an experiment was conducted
Factorial
n! = n(n – 1)(n – 2) . . . 3(2)(1)
Fundamental Counting Principle
f event M can occur in m ways and is followed by event N that can
occur in n ways, then event M followed by event N can occur in m •
n ways.
Independent Events
when the occurrence of one event does not affect the occurrence of a second event
Intersection
the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
Multiplication Rule
P(F∩E) = P(E)∙P(F|E)
Multiplication Rule for Independent Events
P(E∩F) = P(E)∙P(F) if and only if A and B are
independent events.
Mutually Exclusive Events
events that cannot occur at the same time; also called disjoint events
Outcome
a possible result from a probability experiment
Permutation
a way of selecting several things out of a larger group, where order does matter
Permutation Rule
P(n, r) = nPr = n! / (n-r)!
Probability
likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes
Probability Distribution
a way of representing the likelihood of all the possible results of a statistical event.
Random Process (Chance Experiment)
any activity or situation in which there is uncertainty about which of two or more possible outcomes will result
Random Variable
the numerical outcome of a random phenomenon
Sample Space
the set of all possible outcomes in an experiment
Simulation
a way to model random events
Theoretical (Exact) Probability
a ratio of the number of favorable outcomes to the number of possible outcomes
Trial
the single performance of an experiment
Union
everything in both sets
Zero factorial
one