Using the drinking-water example in Section 4.4, show that the posterior hazard probability aftera sequence of n positive laboratory testresults is Po(1-6) Po(1-B)n+(1-Po)an6 where a is the test's false positive rate, ẞ is its false negative rate, and Po is the prior hazard probability adopted before these n results became available. What is the posterior hazard probability given a sequence of three positive results, a false negative rate of 10%, a false positive rate of 5%, and a prior hazard probability Of 0.001?