Bayes' Theorem - detecting a virus from test results. help_outline (a) Assume one person out of 10,000 is infected with HIV, and there is a test in which 2.5% of all people test positive for the virus although they do not really have it. If you test negative on this test, then you definitely do not have HIV. What is the chance of having HIV, assuming you test positive for it?

Bayes' Theorem - detecting a virus from test results. help_outline (a) Assume one person out of 10,000 is infected with HIV, and there is a test in which 2.5% of all people test positive for the virus although they do not really have it. If you test negative on this test, then you definitely do not have HIV. What is the chance of having HIV, assuming you test positive for it?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

A binomial experiment consists of 18 trials. The probability of success on trial 11 is 0.41. What is the probability of success on trial 15? 0.41 or 0.6 or 0.62 or 0.48 or 0.82 or 0.89
How do you find the likelihood ratio?
A certain disease affects about 1 out of 10, 000 people. There is a test to check whether the person has the disease. The test is quite accurate. In particular, we know that • the probability that the test result is positive (suggesting the person has the disease), given that the person does not have the disease, is only 2 percent; • the probability that the test result is negative (suggesting the person does not have the disease), given that the person has the disease, is only 1 percent. A random person gets tested for the disease and the result comes back positive. What is the probability that the person has the disease?
Say you’re a chemical engineer studying whether a certain trace impurity is present in aproduct. An experiment has a probability of 0.80 of detecting the impurity if it is present. Theprobability of not detecting the impurity if it is absent is 0.90. You have reason to believe that40% of products actually contain the impurity. You perform an experiment which detected animpurity – what is the probability that the impurity is not really there?
what is the expected number of failures?
Why we cannot write the probability distribution for a continuous random variable?
You’ve just begun your surgical residency at Sacred Heart hospital. Today you’ve been assigned thesame surgery (Lobotomy) six times. Bringing back fond memories of your favorite statistic class incollege you begin to remember that the probability of success for this type of surgery is 0.70. Being aprofessional, you know that the outcome of any one surgery won’t affect your ability to perform thenext. Given that you’re operating six times today, what is the probability that only four of the six ofthe surgeries are a success?
What does rare outcomes signifies?
How many people do you need to have in a room to reach a 50% chance that at least two people share a birthday? How many individuals do you need to have a >95% chance of at leasttwo people sharing a birthday?
How do I find the p-value from a randomized distribution?
how do i solve this. Prof lecture confused me.
Question: What is meant by 'Chance Error' in statistics?