概率统计c 2_4.pptVIP

Conditional Probability The probabilities assigned to various events depend on what is known about the experimental situation when the assignment is made. Subsequent to the initial assignment, partial information relevant to the outcome of the experiment may become available. Such information may cause us to revise some of our probability assignments. In this section, we examine how the information “an event B has occurred” affects the probability assigned to A. Conditional Probability We will use the notation P(A | B) to represent the conditional probability of A given that the event B has occurred. B is the “conditioning event,” while P(A) is the original, or unconditional probability, of the event A.  As an example, consider the event A that a randomly selected student at your university obtained all desired classes during the previous term’s registration cycle. Presumably P(A) is not very large.  However, suppose the selected student is an athlete who gets special registration priority (the event B). Then P(A | B) should be substantially larger than P(A), although perhaps still not close to 1. Example 24 Complex components are assembled in a plant that uses two different assembly lines, A and A?. Line A uses older equipment than A?, so it is somewhat slower and less reliable. Suppose on a given day line A has assembled 8 components, of which 2 have been identified as defective (B) and 6 as nondefective (B?), whereas A? has produced 1 defective and 9 nondefective components. Example 24 This information is summarized in the accompanying table. Unaware of this information, the sales manager randomly selects 1 of these 18 components for a demonstration.Prior to the demonstrationP(line A component selected) = P(A) =8/18= .44 Example 24 However, if the chosen component turns out to be defective, then the event B has occurred, so the component must have been 1 of the 3 in the B column of the table. Since these 3 components are equally l