help A new process of more accurately detecting anaerobic respiration in cells i

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A new process of more accurately detecting anaerobic respiration in cells is being tested. The new process is important due to its high accuracy, its lack of extensive experimentation, and the fact that it could be used to identify five different categories of organisms: obligate anaerobes, facultative anaerobes, aerotolerant, microaerophiles, and nanaerobes instead of using a single test for each category. The process claims that it can identify obligate anaerobes with 97.8% accuracy facultative anaerobes with 98.1% accuracy, aerotolerant with 95 % accuracy microaerophiles with 96.5% accuracy, and nanaerobes with 99.2% accuracy f any category is not present, the process does not si na samples are prepared or the calibration, or he process and 31% of them contain obligate anaerobes, 27% contain facultative anaerobes, 21% contain microaerophiles, 11% contain nanaerobes, and 10% contain aerotolerant. A test sample is selected randomly. Round your answers to 3 decimal places. (a) What is the probability that the process will signal? The probability (b) If the test signals, what is the probability that microaerophiles are present? The probability....:

Explanation / Answer

P(obligate anaerobes) = 0.31

P(facultative anaerobes) = 0.27

P(microaerophiles) = 0.21

P(nanaerobes) = 0.11

P(aerotolerant) = 0.1

P(signal | obligate anaerobes) = 0.978

P(signal | facultative anaerobes) = 0.981

P(signal | aerotolerant) = 0.959

P(signal | microaerophiles) = 0.965

P(signal | nanaerobes) = 0.992

a) P(signal) = P(signal | obligate anaerobes) * P(obligate anaerobes) + P(signal | facultative anaerobes) * P(facultative anaerobes) + P(signal | aerotolerant) * P(aerotolerant) + P(signal | microaerophiles) * P(microaerophiles) + P(signal | nanaerobes) * P(nanaerobes)

= 0.978 * 0.31 + 0.981 * 0.27 + 0.959 * 0.21 + 0.965 * 0.11 + 0.992 * 0.1

= 0.975

b) P(microaerophiles | signal) = P(signal | microaerophiles) * P(microaerophiles) / P(signal)

= 0.965 * 0.11 / 0.975

= 0.109

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