There are 100 patients in a hospital with a certain disease. Of these, 10 are selected to undergo a drug treatment that increases the percentage cured rate from 50 percent to 75 percent. What is the probability that the patient received a drug treatment if the patient is known to be cured?
Answers
Given : 100 patients in a hospital with a certain disease. Of these, 10 are selected to undergo a drug treatment that increases the percentage cured rate from 50 percent to 75 percent.
To Find : probability that the patient received a drug treatment if the patient is known to be cured?
Solution:
Probability of patient to be cured = 50 % = 1/2
Probability of patient to be cured if undergo a drug treatment = 75 % = 3/4
Total Patient = 100
under go drug treatment = 10/100 = 1/10
Other = 90/100 = 9/10
Patient to be cured under drug treatment = (1/10) * 3/4 = 3/40
Patient to be cured with out under drug treatment = (9/10) * 1/2 = 9/20
= 18/40
Total = 3/40 + 18/40 = 21/40
the patient received a drug treatment if the patient is known to be cured
= (3/40)/(21/40)
= 1/7
1/7 is the probability that the patient received a drug treatment if the patient is known to be cured
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