Question 1180305: A few people who have a particular disease take part in a medical trial that tests the effect of a medicine on the disease. Half the people are given medicine and the other half are given sugar pills, which have no effect on the disease. The medicine has a 60% chance of curing someone, but people who do not get the medicine still have a 10% chance of getting well.
The probability that a person gets well is ? %, and the probability that the person was cured because of the medicine is
? %
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 0.5 are given the medicine, which has a 0.60 probability of cure, so that is 0.30 of the total who will be cured.
plus
0.5*0.10=0.05.
The probability the person got well over all is 35%
C=== NC===Tot
M= 60 ==40 ==100
P = 10== 90= 100
Tot-70--130--200
The last part is not clear. There is a 60% probability someone was cured because of the medicine. That is known.
BUT, given that someone was cured, the probability that they had taken the medicine was 6/7 or 86%. That is a different statement.
This is an extremely important distinction to make in medicine and other places. Just because B followed A doesn't mean that A caused B.
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