
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
In a small village, one of every 200 people is known to carry a particular genetic mutation without any visible symptoms. A diagnostic test is used to detect this mutation. The test is 100% sensitive, meaning it always correctly identifies those with the mutation. However, the test has a false positive rate of 5%. Let $p$ be the probability that a person who tests positive for the mutation actually has the mutation. What is $p$?
A) $\frac{1}{10}$
B) $\frac{20}{219}$
C) $\frac{1}{20}$
D) $\frac{10}{219}$
E) $\frac{5}{100}$

Present the answer in LaTex format: \boxed{Your answer}
user