Question

⦁   Suppose in August the Covid-19 situation has calmed down. Since not everyone shows symptoms and...

⦁   Suppose in August the Covid-19 situation has calmed down. Since not everyone shows symptoms and some symptoms could have been a different pneumonia we might use an anti-body test to see if people have had the disease. Let’s assume by August 40% of the US has had the disease. The anti-body test is not perfect. Some people will get “false positives” or “false negatives”. 90% of people who test positive will actually have had the disease. 95% of people who test negative will have not had the disease.

3A) What is the “prior probability” of a random person having had the disease? (That is, before giving the person the test what is your best guess for the likelihood they had the disease?)


3B) If the person receives a positive anti-body test what is the posterior probability of them having had the disease? (That is, what is your best guess for the likelihood they had the disease given they tested positive on the anti-body test?)

3C) If the person receives a negative anti-body test what is the posterior probability of them having had the disease? (That is, what is your best guess for the likelihood they had the disease given they tested negative on the anti-body test?)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose that a test for determining whether a person has been infected with COVID-19 has a...
Suppose that a test for determining whether a person has been infected with COVID-19 has a 20% rate of false positives (i.e. in 20% of applications, the test falsely indicates that a person has been infected with COVID-19 when they actually have not). Now, consider the likelihood that when 100 healthy people are tested, the test falsely indicates that between 10 and 30 of them are infected. a. Calculate the expected number of false positives (μ) in a sample of...
suppose that 1% of the us population is a carrier of covid -19.Also suppose that a...
suppose that 1% of the us population is a carrier of covid -19.Also suppose that a person that has covid-19 that the test they are given will have a positive test result of 91.9% of the time and a false negative result of 8.1% of the time.Also suppose that if a person doesn't have covid-19 then the test will result in a negative result of 99% of the time and a false positive of 1% of the time. A) Draw...
There is a population where no one has any COVID symptoms. Even though everyone in the...
There is a population where no one has any COVID symptoms. Even though everyone in the population is asymptomatic, in reality 5% of this population is a carrier of the virus. There is a test that accurately identifies 90% of the people who are carrying the virus. If a person does not carry the virus the test identifies that accurately 85% of the time. A random person in this population is given the test, and the test comes back positive...
The probability that a person actually has the disease is 0.3, implying that out of 1000...
The probability that a person actually has the disease is 0.3, implying that out of 1000 people, 30 people have the disease. A new test has a false positive probability of 0.01 and a false negative probability of 0.02. A person is given the test and the result is positive, what is the probability they actually have the disease?
Suppose that a test for determining whether a person has been infected with COVID-19 has a...
Suppose that a test for determining whether a person has been infected with COVID-19 has a 20% rate of false positives (i.e. in 20% of applications, the test falsely indicates that a person has been infected with COVID-19 when they actually have not). Now, consider the likelihood that when 100 healthy people are tested, the test falsely indicates that between 10 and 30 of them are infected. c. Before you use the normal approximation to calculate P(10 ≤ x≤ 30),...
A certain genetic condition affects 5% of the population in a city of 10,000. Suppose there...
A certain genetic condition affects 5% of the population in a city of 10,000. Suppose there is a test for the condition that has an error rate of 1% (i.e., 1% false negatives and 1% false positives). Consider the values that would complete the table below.       Has condition       Does not have condition       Totals Test positive Test negative Totals What is the probability (as a percentage) that a person does not have the condition if he or she...
Suppose you are analyzing a test for a blood disease where • 94% of people with...
Suppose you are analyzing a test for a blood disease where • 94% of people with the disease test positive. • Only 0.5% of the population has this disease. • The false-positive rate is 0.1%. (a) What is the test’s precision, that is the probability that a person with a positive test has the disease? (b) What is the accuracy of the test, that is the probability that either a person tests positive AND has the disease OR a person...
The test for a disease has a false positive rate of 5% and a false negative...
The test for a disease has a false positive rate of 5% and a false negative rate of 3%.  Suppose a person to be test has the disease with probability 20%. If the test is positive, what is the revised probability that the person has the disease? If the test is negative, what is the revised probability that the person has the disease? If the test is negative, what is the revised probability that the person does not have the disease?...
A person takes a test to detect the occurence of a disease. The test’s characteristics are...
A person takes a test to detect the occurence of a disease. The test’s characteristics are such that a person testing positive has actually a 70% chance actually having contracted the disease. Meaning that a person not having contracted the disease has a 30% chance of testing positive to it. The test’s results are used to allow a person to exit a quarantine – because having the disease makes them immune to it and they are no longer in risk...
According to the CDC and NIH, approximately 1 in 10,000 people have Huntington's disease. Suppose a...
According to the CDC and NIH, approximately 1 in 10,000 people have Huntington's disease. Suppose a new test for Huntington's disease is developed. The probability of a false positive is 0.001, and the probability of a false negative is 0.006. If a randomly selected individual is tested using this new test and the result is positive, what is the probability that the individual actually has Huntington's disease? Is this test good enough to consider using?