Suppose that the reliability of a HIV test is specified as follows: Of people having HIV. 90% of the test detects the disease but 10% go undetected. Of people free of HIV, 99% of the test are judged HIV-ive but 1% are diagnosed as showing HIV+ive. From a large population of which only 0.1% have HIV one person is selected at random, given the HIV test, and the pathologist reports him/her as HIV+ive. What is the probability that the person actually has HIV?

Explanation

To solve the problem, we will use Bayes' theorem to find the probability that a person actually has HIV given that they tested positive for it.

### Step-by-Step Solution:

1. **Define Events**:
- Let \( E \): the event that the person has HIV.
- Let \( F \): the event that the person does not have HIV.
- Let \( G \): the event that the test result is positive.
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