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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.

**Addition rules for probability**

: 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.