A new process of more accurately detecting anaerobic respirationin cells is bein

Question

A new process of more accurately detecting anaerobic respirationin cells is being tested. The new process is important due to itshigh accuracy, its lack of extensive experimentation, and the factthat it could be used to identify five different categories oforganisms: obligate anaerobes, facultative anaerobes, aerotolerant,microaerophiles, and nanaerobes instead of using a single test foreach category. The process claims that it can identify obligateanaerobes with 97.8% accuracy, facultative anaerobes with 98.1%accuracy, aerotolerant with 95.9% accuracy, microaerophiles with96.5% accuracy, and nanaerobes with 99.2% accuracy. If any categoryis not present, the process does not signal. Samples are preparedfor the calabration of the process and 31% of them contain obligateanaerobes, 27% contain facultative anaerobes, 21% containmicroaerophiles, 11% contain nanaerobes, and 10% containaerotolerant. A test sample is selected randomly.

Round the answers to 3 significant digits.

a) What is the probability that the process will signal?

b) If the test signals, what is the probability thatmicroaerophiles are present?

Explanation / Answer

31% of them contain obligate anaerobes, P(O ) = 0.31 27% contain facultative anaerobes = P(F) = 0.27 21% contain microaerophiles, P(M) = 0.21 11% contain nanaerobes, P(N) = 0.11 10% contain aerotolerant, P(A) = 0.1

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