Question 1180211
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%**.