Question

No (Baye's Theorem) A carbon monoxide (CO) detector can detect the presence of CO with 95% probability if there exist trace amounts of CO. However, it gives a false alarm with 5% probability when no CO is present. This detector is employed to inspect furnaces for leakage of CO, Assume that 1% of furnaces have a CO leakage problem. a. Find the total probability that the detector gives an alarm when a furnace is randomly checked. b. Find the probability that a furnace is leaking CO given that the detector gave an alarm during the inspection of the furnace c. Is this result surprising? Write a sentence or two explaining this result.

Answer 1

a)P(alarm)=P(trace of CO and alarm)+P(no trace of CO and alarm)=0.01*0.95+0.99*0.05=0.059

b)

P(CO leakage given alarm)=P(trace of CO leakage and alarm)/P(alarm =0.01*0.95/0.059=0.161017

c)

No ;as we can see that probability of a CO leakage is smaller and probability of false positive(0.05) is higher therefore total number of false alrm will be higher in comparison to true alarm.Therefore given a alarm rings it is higher probability that no CO leakage then CO leakage.