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7.5 Conditional Probability and Independent Events Copyright © Cengage Learning. All rights reserved.

More on Tree Diagrams

Applied Example 6 – Quality Control The panels for the Pulsar 32-inch widescreen LCD HDTVs are manufactured in three locations and then shipped to the main plant of Vista Vision for final assembly. Plants A, B, and C supply 50%, 30%, and 20%, respectively, of the panels used by the company. The quality-control department of the company has determined that 1% of the panels produced by Plant A are defective, whereas 2% of the panels produced by Plants B and C are defective. What is the probability that a randomly selected Pulsar 32-inch HDTV will have a defective panel?

Applied Example 6 – Solution Let A, B, and C denote the events that the HDTV chosen has a panel manufactured in Plant A, Plant B, and Plant C, respectively. Also, let D denote the event that a HDTV has a defective panel. Using the given information, we draw the tree diagram shown in Figure 19. (The events that result in a HDTV with a defective panel being selected are circled.) Tree diagram showing the probabilities of producing defective panels at each plant Figure 19

Applied Example 6 – Solution cont’d Taking the product of the probabilities along each branch leading to such an event and then adding them, we obtain the probability that a HDTV chosen at random has a defective panel. Thus, the required probability is given by (.5)(.01) + (.3)(.02) + (.2)(.02) = .005 + .006 + .004 = .015

Practice p. 408 Self-Check Exercises #2