SOLUTION: 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 ar

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Question 1180211: 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 ?%.
what goes in the ?'s
Answer by CPhill(1987) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how to solve this problem using probability:
**1. Probability of Getting Well:**
* **Medicine Group:**
* Probability of getting medicine: 0.5 (half the people)
* Probability of cure with medicine: 0.6
* Probability of cure in medicine group: 0.5 * 0.6 = 0.3
* **Placebo (Sugar Pill) Group:**
* Probability of getting placebo: 0.5 (the other half)
* Probability of getting well without medicine: 0.1
* Probability of getting well in placebo group: 0.5 * 0.1 = 0.05
* **Total Probability of Getting Well:**
* Add the probabilities from both groups: 0.3 + 0.05 = 0.35
* **Convert to Percentage:** 0.35 * 100% = 35%
**2. Probability of Being Cured by the Medicine (Conditional Probability):**
We want to find the probability that a person was cured by the medicine *given* that they got well. We use conditional probability:
P(Medicine Cure | Got Well) = P(Medicine Cure AND Got Well) / P(Got Well)
* P(Medicine Cure AND Got Well) = 0.3 (calculated above)
* P(Got Well) = 0.35 (calculated above)
P(Medicine Cure | Got Well) = 0.3 / 0.35 ≈ 0.8571
* **Convert to Percentage:** 0.8571 * 100% ≈ 85.71%
**Answers:**
* The probability that a person gets well is **35%**.
* The probability that the person was cured because of the medicine is approximately **85.71%**.