Correct way to interpret conditional probability wording

Question

I would like to double check my interpretation of a probability question.

2% of a population have a given medical condition. There is a medical test for that condition with 90% accuracy.

If a person tests positive, what is the probability the person actually has the condition?

Based on this, I have determined that the question is looking for P(D|pos)

Let pos = positive test result

Let D = condition of having the medical condition

• P(D) = 0.02
• P(pos|D) = 0.9
• P(pos|Dc) = 0.1

Question:

1. Does my interpretation look correct?
2. Have I found all the correct ingredients?

Answer 1

EDIT: Assuming that, with the term "90% Accuracy", we mean that Both Sensitivity and Specificity are 90%,

Yes, your interpretation is correct. Using your ingredients and Conditional probability's definition you get

$$\mathbb{P}[D|\text{pos}]=\frac{0.02\times0.90}{0.02\times0.90+0.98\times0.1}\approx15.52\%$$