概率与统计（英文）chapter 2.ppt

2 probability Sample Space and Events Axioms, Interpretations, and Properties of Probability Counting Techniques Conditional Probability Independence Introduction The term probability refers to the study of randomness and uncertainty. In any situation in which one of a number of possible es may occur, the theory of probability provides methods for quantifying the chances, or likelihoods, associated with the various es. The language of probability is constantly used in an informal manner in both written and spoken contexts. In this chapter, we introduce some elementary probability concepts, indicate how probabilities can be interpreted, and show how the rules of probability can be applied pute 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. Sample Spaces and Events An experiment is any action or process that generates observations. For examples, tossing a coin once or several times, selecting a card or cards from a deck, weighing a loaf of bread, ascertaining muting time from home to work on particular morning, obtaining blood types from a group of individuals, etc. Random experiment Sample space and sample point Definition : The sample space of an experiment, denoted by S , or Ω,is the set of all possible es of that experiment, and sample point of the sample space, denoted by s , is a e of the experiment. Example : The simplest experiment to which probability applies is one with two possible es. One such experiment consists of examining a single fuse to see whether it is defective . The sample space for this experiment can be abbreviated as S ={N,D}, where N represents not defective, D represents defective, and the braces are used to enclose the elements of a set. Another such experiment would involve