2.4.31. medical records show that 0.01% of the general adult population not belonging to a high-risk group (for example, intravenous drug users) are hiv-positive. blood tests for the virus are 99.9% accurate when given to someone infected and 99.99% accurate when given to someone not infected. what is the probability that a random adult not in a highrisk group will test positive for the hiv virus? larsen, richard j.. an introduction to mathematical statistics and its applications (p. 44). pearson education. kindle edition.

The probability is 0.00019989

Step-by-step explanation:

We are going to define the conditional probability as :

Where P(A,B) is the probability of the event (A∩B).

Let's define the following events :

B : ''The HIV test is positive''

A : ''The adult is infected''

Also we define :

Where is the event where A does not occur.

In the exercise :

Where

represents the test accuracy

We are ask about P(B).

We write :

P(B) = P{ [(B∩A)∪[B∩(A^{c})]}

P(B) = P(B∩A) +P[B∩(A^{c})]

Using the conditional equations

the 4th choice is the correct one

step-by-step explanation: