Question

Pleas solve this problem step by step.

In a certain hospital, 20 percent of the patient with a certain disease underwent a drug treatment that increases the percentage cured form 50 percent to 75 percent.

(a)  Calculate the resultant percentage cured rate of the disease in the hospital.

(b) Mr. Kim is one of the patient who has been cured of the disease. What is the probability that Mr. Kim had undergone the drug treatment?

Answer 1

a) 20 % of the patients with a certain disease underwent drug treatment which has a cure rate of 75% and rest of the 80% of patients didn't undergo any drug treatment, hence there cure rate is still 50%.

Hence, Resultant %age cure rate of the disease in the hospital = 20% * 75% + 80% * 50% = 0.2*0.75 + 0.80*0.50 = 0.15 + 0.4 = 0.55

55% is the resultant percentage cure rate of the disease in the hospital.

b) We need to find the P(Mr. Kim had undergone the drug treatment given that Mr. Kim is one of the patient who has been cured of the disease) = P(Drug Treatment | Cured)

Hence, the probability of the same is 0.273