# Danny Lee Professor James W. Chaires Math 221                       Danny Lee Professor James W. Chaires Math 221

Chapter 5 Definitions Experiment:

An activity or measurement that results in an outcome

Sample Space:

All possible outcomes of an experiment.

Event:

one or more of the possible outcomes of an experiment; a subset of the sample space.

Probability:

a number between 0 and 1 which expresses the chance that an event will occur.

Classical probability:

For outcomes that are equally likely, Probability = Number of possible outcomes in which the event occurs, divided by the total number of possible outcomes

Relative frequency probability

: For a very large number of trials. Probability = Number of trials in which the event occurs, divided by the total number of trials.

Subjective probabilities

: Where the subjective approach to probability is judgmental, representing the degree to which one happens to believe that an event will or will not happen,( hunches or educated guesses).

Odds:

A way of expressing the likelihood that something will happen. Mutually exclusive events: If one event occurs the other cannot occur. An event (e.g., A) and it’s compliment ( A’) are always mutually exclusive.

Exhaustive Events

: A set of events that includes all the possible outcomes of an experiment.

Intersection of Events

: Two or more events occur at the same time.

Union of Events

: At least one of a number of possible events occurs.

: Occasions where we wish to determine the probability that one or more of several events will occur in an experiment.

Rule of addition when events are mutually exclusive

: P(A or B) = P(A) + P(B)

General rule of addition when events are not mutually exclusive

: P(A or B) = P(A) +P(B) – P(A and B)

Marginal Probability

: The probability that a given event will occur. No other events are taken into consideration.

Joint Probability

: The probability that two or more events will all occur.

Conditional Probability

: The probability that an event will occur, given that another event has already happened.

Independent events

: When the occurrence of one event has no effect on the probability that another will occur.

Dependent events:

When the occurrence of one event changes the probability that another will occur.

Multiplication rule when events are independent

: P(A and B) = P(A) P(B)

Multiplication rule when events are not independent

:

    P(A and B) = P(A) x P(B\A)

Bayes’ Theorem for the revision of probability

: 1.

Events A and B: Probability of A, given that event B has occurred: P(A\B) = P(A and B) / P(B) = P(A) * P(B\A) -------------------------------------------- P(A) * P(B\A)] + [P(A’) * P(B\A’)

Factorial

: In which the product (5 x 4 x 3 x 2 x 1) can be described as 5!. For example, 3! Is the same as 3 x 2 x 1. The exclamation point is just a mathematical way of saving space.

Permutations:

refers to the number of different ways in which objects can be arranged in order.

Combinations

: Unlike permutations, combinations consider only the possible sets of objects, regardless of the order in which the members of the set are arranged.