Home >
Probability >
CBSE >
0ffe0bdc-7841-49f4-acdc-c445ef9c908c
Not the exact question you were looking for?
Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.
Probability
Oswaal
CBSE
Grade 12
Question:
Suppose that the reliability of a HIV test is specified as follows: Of people having HIV, 90% of the test detect the disease but 10% go undetected. Of people free of HIV, 99% of the test are judged HIV negative but 1% are diagnosed as HIV positive. 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 positive. What is the probability that the person is actually HIV positive?
Step-by-Step Solution
Key Concept: Let E1: person has HIV (0.001), E2: person does not have HIV (0.999). A: test is HIV positive. P(A|E1) = 0.90, P(A|E2) = 0.01. By Bayes Theorem: P(E1|A) = (0.001 * 0.90) / (0.001 * 0.90 + 0.999 * 0.01) = 0.0009 / (0.0009 + 0.00999) = 90 / 1089 = 10/121.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer:
Mathbee AI Mentor (Free Demo)
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.
Master Probability with Mathbee
Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.