Question 1114805
this is what i think it will be.


the probability that a patient receives the drug treatment is 10/100 = .1


the formula for that is p(D) = .1


10% of the time, the patient is cured using the drug, and 90% of the time the patient is cured without taking the drug.


the formula for that is p(C) = .1 * .75 + .9 * .5 = .525


the probability that a person is cured and has taken the drug is .1 * .75 = .075


the formula for that is p(C and D) = .075


given that a person is cured, what is the probability that the person took the drug.


the formula for that is p(D given C) = p(C and D) / p(C).


that becomes p(D given C) = .075 / .525 = .1428571429.


i usually try an experiment to see if what i did is reasonable.


my experiment for this problem is as follows.


assume 1000 patients.


10% of them receive the drug and 90% of them don't.


that makes 100 who received the drug and 900 who didn't.


75% of the ones who took the drug are cured = 75


50% of the ones who didn't take the drug are cured = 450.


total number of cured patients = 525.


525/1000 = .525, so p(C) looks like an accurate ratio.


given that a person is cured, what is the probability that the person took the drug.


525 were cured and, out of them, 75 took the drug.


75/525 = .1428571429, so p(D given C) looks good as well.


75 patients out of the 1000 gook the drug and were cured.


p(D and C) = 75 / 1000 = .075, so that ratio looks good as well.


the solution looks reasonable, so i would go with that.