An automatic breathing apparatus (B) used in anesthesia fails withprobability P

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An automatic breathing apparatus (B) used in anesthesia fails withprobability Pb. A failure means death to thepatient unless a monitor system (M) detects the failure and alertsthe physician. The monitor system fails with probabilityPm. The failure of the systems are independentevents. Professor X, an M.D. at Hevardi Medical School,argues that if PM >PB installation of M isuseless. Show that Prof. X needs to take a course onprobability theory by computing the probability of a patient dyingwith and without the monitor system in place. TakePM=0.1=2PB.

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