A medical laboratory uses three machines (named M1, M2, and M3, respectively) to measure prostate-specific antigen (PSA) levels in selected blood samples from adult men; Elevated PSA levels have been associated with the presence of prostate cancer. Suppose the machine M1 has a 0.01 probability of giving an incorrect PSA level, that the M2 machine has a 0.02 probability of give an incorrect PSA level and the M3 machine has 0.03 probability of giving a PSA level incorrect. Also, suppose the M1 machine performs 20% of the PSA analyzes done by this lab doctor, that the M2 machine performs 50% of the PSA analyses, and that the M3 machine performs 30% of the PSA analyses. PSA (a) Find the probability that a PSA analysis performed by this medical laboratory is performed correctly. (b) Given that a given PSA analysis was performed incorrectly, what is the value of the probability of that this PSA analysis was performed by the M1 machine or by the M2 machine?

A medical laboratory uses three machines (named M1, M2, and M3, respectively) to measure prostate-specific antigen (PSA) levels in selected blood samples from adult men; Elevated PSA levels have been associated with the presence of prostate cancer. Suppose the machine M1 has a 0.01 probability of giving an incorrect PSA level, that the M2 machine has a 0.02 probability of give an incorrect PSA level and the M3 machine has 0.03 probability of giving a PSA level incorrect. Also, suppose the M1 machine performs 20% of the PSA analyzes done by this lab doctor, that the M2 machine performs 50% of the PSA analyses, and that the M3 machine performs 30% of the PSA analyses. PSA (a) Find the probability that a PSA analysis performed by this medical laboratory is performed correctly. (b) Given that a given PSA analysis was performed incorrectly, what is the value of the probability of that this PSA analysis was performed by the M1 machine or by the M2 machine?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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