hw3_scanned

# hw3_scanned - Sec 3.7 ~ri ho eet ba the rk ity the uc ing...

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Sec 3.7 Bayes'Theorem 77 ~ri- 3.78 Two firms V and W consider bidding on a road- Iho building job, which mayor may not be awarded de- leet pending on the amounts of the bids. Firm V submits ba- the Irk- lity 3 a bid and the probability is - that it will get the job 4 3 provided firm W does not bid. The probability is 4 that W will bid, and if it does, the probability that V will 1 the get the job is only 3 luc- ring (a) What is the probability that V will get the job? (b) If V gets the job, what is the probability that W did not bid? W% rom cars ires, with 3.79 Engineers in charge of maintaining our nuclear fleet must continually check for corrosion inside the pipes that are part of the cooling systems. The inside con- dition of the pipes cannot be observed directly but a nondestructive test can give an indication of possible ,ility from corrosion. This test is not infallible. The test has prob- ability 0.7 ofdetecting corrosion when it is present but it also has probability 0.2 of falsely indicating internal corrosion. Suppose the probability that any section of 3.16 pipe has internal corrosion is 0.1. (a) Determine the probability that a section of pipe has internal corrosion. given that the test indicates its presence. (b) Determine the probability that a section ofpipe has internal corrosion, given that the test is negative. 3.80 An East Coast manufacturer of printed circuit boards exposes all finished boards to an online automated ver- ification test. During one period, 900 boards were com- pleted and 890 passed the test. The test is not infallible. Of 30 boards intentionally made to have noticeable de- fects, 25 were detected by the test. Use the relative fre- quencies to approximate the conditional probabilities needed below. (a) Give an approximate value for P[Pass test I board has defects]. (b) Explain why your answer in part a may be too small. (c) Give an approximate value for the probability that a manufactured board will have defects. In order to answer the question, you need information about the conditional probability that a good board will fail the test. This is important to know but was not available at the time an answer was required. To proceed, you can assume that this probability is zero. (d) Approximate the probability that a board has de- fects given that it passed the automated test. Id the ns ac- prob- initial ir was . Do's and Don'ts Do's I. Begin by creating a sample space S which specifies all possible outcomes. 2. Always assign probabilities to events that satisfy the axioms ofprobability. In the discrete case, the possible outcomes can be arranged in a sequence. The axioms are then automatically satisfied when probability Pi is assigned to the ith outcome, where O".S Pi and Pi = 1 all outcomes in S and the probability of any event A is defined as peA) = Pi all outcomes in A 3. Combine the probabilities of events according to rules of probability.
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hw3_scanned - Sec 3.7 ~ri ho eet ba the rk ity the uc ing...

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