Let's say the probability of people having the mutant X-gene,
P(X) is $0.01$. There's a test to detect the gene which results in a positive or negative outcome. In case of people who actually have the X-gene this test results positive $90\%$ of the time. In the case of people who don't have the X-gene, this test results negative $90\%$ of the time.
The question to answer is:
Given that the test comes out positive for a person, what is the probability of that person being a mutant?
Let's try to visualize this scenario. In the figure below the box represents all people. Inside the box, the purple circle represents people who actually have the X-gene, ie, $1\%$ of all people. The red highlighted area is the $90\%$ of the purple circle, and represents people who actually have the X-gene and test positive. The green highlighted is $10\%$ of the area of the box (ie, $10\%$ of all people), and represents people who don't have the X-gene and test positive.