Statistics Probability Flashcards (copy)

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