Statistics: Principles and Methods, 7th Edition

4

Probability

1 Probability of an Event

2 Methods of Assigning Probability

3 Event Operations and Two Laws of Probability

4 Conditional Probability and Independence

5 Bayes' Theorem

6 Random Sampling from a Finite Population

Uncertainty of Weather Forecasts

Today's forecast: Increasing cloudiness with a 25% chance of snow.

Probabilities express the chance of events that cannot be predicted with certainty. Even unlikely events sometimes occur.

In Chapter 1, we introduced the notions of sample and statistical population in the context of investigations where the outcomes exhibit variation. Although complete knowledge of the statistical population remains the target of an investigation, we typically only have the partial information contained in a sample. Chapter 2 focused on some methods for describing the salient features of a data set by graphical presentations and calculation of the mean, standard deviation, and other summary statistics. However, when the data set represents a sample from a statistical population, its description is only a preliminary part of a statistical analysis. Our major goal is to make generalizations or inferences about the target population on the basis of information obtained from the sample data. It is the subject of probability that is essential for understanding the reasoning that leads to such generalizations.

In everyday conversations, we all ...