1.The pregnancy example was completely contrived. In fact, most pregnancy tests today do not have such high rates of false positives. The “accuracy rate” is usually determined by computing the percent of correct answers the test gives; that is, the combined percent of positive results for positive cases and negative results for negative cases (versus false positives and false negatives). Recompute the posterior probability for being pregnant based on an accuracy rate of 90% defined in this manner. Assume that false positives and false negatives occur equally frequently under this 90% rate. What changes in the calculation?
1.Determine the posterior probability that a 30-year-old male has prostate cancer, given (1) a positive PSA test result; (2) a 90% accuracy rate (as defined in the pregnancy example), coupled with a 90% false positive rate; and (3) a prior probability of .00001 for a 30-year-old male having prostate cancer. Based on the result, why might a physician consider not testing a 30-year-old male using the PSA test?
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