Question 1180343: 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 ? %
The probability that the person was cured because of the medicine is ? %
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Let's say that 1000 people are in the medical trial. Half (500) are given the actual medicine, while the other 500 are given the placebo sugar pill.
Of the 500 people who took the actual medicine, we have 60% of them getting better. So we had 0.60*500 = 300 people get better. The remaining 200 unfortunately didn't get cured even though they took the actual medicine.
Of those who took the sugar pill, 10% got better. So we have 0.10*500 = 50 people get better in this group while the remaining 500-50 = 450 did not get better.
It's recommended you make up a table (shown below) to help organize the results. This step is optional of course.
| Cured | Not Cured | Total | | Took Medicine | 300 | 200 | 500 | | Took Sugar Pill | 50 | 450 | 500 | | Total | 350 | 650 | 1000 |
In the table, we see that 300 got cured from the actual medicine, and 50 got cured from the placebo leading to 300+50 = 350 cured overall. The probability of a cure is 350/1000 = 0.35 = 35%
That takes care of the first part.
Now onto the second part. Focus on the first column only. We have 300 people cured because of the medicine out of 350 cures total.
We then get 300/350 = 0.85714 approximately, which converts to 85.71% roughly.
This represents the percentage of people who got cured, and also got the actual medicine.
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Answers:
The probability that a person gets well is 35%
The probability that the person was cured because of the medicine is 85.71% (approximate)
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