Danny Lee Professor James W. Chaires Math 221
Chapter 5 Definitions Experiment:
An activity or measurement that results in an outcome
All possible outcomes of an experiment.
one or more of the possible outcomes of an experiment; a subset of the sample space.
a number between 0 and 1 which expresses the chance that an event will occur.
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.
: 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).
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.
: 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)
: The probability that a given event will occur. No other events are taken into consideration.
: The probability that two or more events will all occur.
: The probability that an event will occur, given that another event has already happened.
: When the occurrence of one event has no effect on the probability that another will occur.
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
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’)
: 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.
refers to the number of different ways in which objects can be arranged in order.
: Unlike permutations, combinations consider only the possible sets of objects, regardless of the order in which the members of the set are arranged.