Content

• 2.1 sample spaces and events
• 2.2 axioms interpretations and properties of probability
• 2.3 Counting Techniques
• 2.4 Conditional probability
• 2.5 Independence

What is probability

• The term probability refers to the study of randomness and uncertainty.
• In any situation in which one of a number of possible outcomes may occur, the discipline of probability provides methods for quantifying the chances, or likelihoods, associated with the various outcomes.
• The language of probability is constantly used in an informal manner in both written and spoken contexts.

Examples

• “It is likely that the Dow Jones average will increase by the end of the year,”
• “There is a 50-50 chance that the incumbent will seek reelection,”
• “There will probably be at least one section of that course offered next year,”
• “The odds favor a quick settlement of the strike,”
• “It is expected that at least 20,000 concert tickets will be sold.”

Goals of this chapter

• introduce some elementary probability concepts
• indicate how probabilities can be interpreted
• show how the rules of probability can be applied to compute the probabilities of many interesting events.
• The methodology of probability will then permit us to express in precise language such informal statements as those given above.

Remark on history

The study of probability as a branch of mathematics goes back over 300 years, where it had its genesis in connection with questions involving games of chance. Many books are devoted exclusively to probability, but our objective here is to cover only that part of the subject that has the most direct bearing on problems of statistical inference.