A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?

Explanation

To solve the problem, we will use Bayes' theorem to find the probability that a person has the disease given that their test result is positive.

### Step-by-Step Solution:

1. **Define Events**:
- Let \( D \) be the event that a person has the disease.
- Let \( P \) be the event that the test result is positive.

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