## **Core Concept**
The problem involves calculating the positive predictive value (PPV) of a diagnostic test. The PPV is the probability that a person with a positive test result actually has the disease. It depends on the test's sensitivity, specificity, and the disease prevalence in the population.

## **Why the Correct Answer is Right**
To calculate the PPV, we use the formula:
[ PPV = frac{Prevalence times Sensitivity}{Prevalence times Sensitivity + (1 - Prevalence) times (1 - Specificity)} ]
Given:
- Sensitivity = 0.90
- Specificity = 0.90
- Prevalence = 10% or 0.10
Substituting these values:
[ PPV = frac{0.10 times 0.90}{0.10 times 0.90 + (1 - 0.10) times (1 - 0.90)} ]
[ PPV = frac{0.09}{0.09 + 0.90 times 0.10} ]
[ PPV = frac{0.09}{0.09 + 0.09} ]
[ PPV = frac{0.09}{0.18} ]
[ PPV = 0.50 ]
So, the probability that a person positive to this test has the disease is 0.50 or 50%.

## **Why Each Wrong Option is Incorrect**
- **Option A:** This option is incorrect because it does not match our calculated PPV of 0.50.
- **Option B:** This option is incorrect for the same reason as Option A; the calculation does not support this value.
- **Option D:** This option suggests a PPV of 0.90, which overestimates the actual probability given the provided sensitivity, specificity, and prevalence.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that the PPV of a test increases with the prevalence of the disease in the population. If this test were applied to a population with a higher prevalence of the disease, the PPV would increase, meaning a positive test result would be more likely to indicate the presence of the disease.

## **Correct Answer:** C. 0.50