Chapter 4

Equally likely outcomes

A probability assignment based on equally likely outcomes uses the formula: probability of event = (# of outcomes favorable to event)/(Total # of outcomes)

Intuition

A probability assignment based on intuition incorporates past experience, judgment, or opinion to estimate the likelihood of an event.

Relative Frequency

A probability assignment based on relative frequency uses the formula: Probability of event = relative frequency = f/n where f is the frequency of the event occurrence in a sample of n observations

Simple Event

A simple event is one particular outcome of a statistical experiment The sum of the probabilities of all simple events in a sample space must equal 1

Statistical Experiment

A statistical experiment or statistical observation can be thought of as any random activity that results in a definite outcome.

Event

An event is a collection of one or more outcomes of a statistical experiment or observation.

Probability of A

If P(A) = 1, event A is certain to occur. If P(A) = 0, event A is certain not to occur.

Law of large numbers

In the long run, as the sample size increases and increases, the relative frequencies of outcomes get closer and closer to the theoretical (or actual) probability value.

Probability

Probability is a numerical measure between 0 and 1 that describes the likelihood that an event will occur. Probabilities closer to 1 indicate that the event is more likely to occur. Probabilities closer to 0 indicate that the event is less likely to occur.

probability vs statistics

Probability is the field of study that makes statements about what will occur when samples are drawn from a known population Statistics is the field of study that describes how samples are to be obtained and how inference are to be made about an unknown population

Sample Space

The set of all simple events constitutes the sample space of an experiment

Independent Events

Two events are independent if the occurrence or nonoccurrence of one event does NOT change the probability that the other event will occur **Multiplication rule for independent events**

Mutually Exclusive

Two events are mutually exclusive or disjoint if they cannot occur together. In particular, events A and B are mutually exclusive if P(A and B) = 0