Twocombinationdrugtherapies(TreatmentAandTreatmentB)have been developed for eradicating Helicobacter pylori in human patients. The effectiveness of these treatments depends on...

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Twocombinationdrugtherapies(TreatmentAandTreatmentB)have beendeveloped for eradicating Helicobacter pylori in humanpatients. The effectiveness of these treatments depends on whetheror not the patient is resistant to the chemical compoundMetronidazole, but apatientâ€™s resistance status is not routinelydetermined before beginningtreatment. Treatment A successfullyeradicates Helicobacter pylori in 92% of resistantpatients and 87% of non-resistant patients. The correspondingproportions for Treatment B are 75% and 95%.
(i) Denote by Î¸ (0 < Î¸ < 1) the proportion of the affectedpopulation that is resistant. If a patient from this population isunsuccessfully treated with Treatment B, write down an expressionfor the probability that the patient is resistant.
(ii) For what values of Î¸ would a greater proportion of patientsfrom this population be successfully treated by Treatment B than byTreatment A?
(iii) Suppose that Î¸ = 0.2. If 20 patients, selected at randomfrom the affected population, are independently treated withTreatment B, find the probability that at least 18 of them will betreated successfully.

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Solution Let R represent the event that the patient is resistant A represent the event that Treatment A is successful in treating the patient and B represent the event that Treatment B is successful treating the patient Then trivially RC represents the event that the patient is nonresistant AC See Answer

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