A diagnostic test has a 95% probability of giving a positive result when given to a...

A diagnostic test has a 95% probability of giving a positive result when given to a person who has a certain disease. It has a 10% probability of giving a (false) positive result when given to a person who doesn’t have the disease. It is estimated that 15% of the population suffers from this disease.

(a) What is the probability that a test result is positive?

(b) A person recieves a positive test result. What is the probability that this person actually has the disease? (probability of a true positive)

(c) A person recieves a positive test result. What is the probability that this person doesn’t actually have the disease? (probability of a false negative)

Expert Solution

P(having the disease) = 0.15

P(positive test | have the disease) = 0.95

P(positive test | don't have the disease) = 0.1

a) P(positive test result) = P(positive test | have the disease) * P(have the disease) + P(positive test | don't have the disease) * P(don't have the disease)

= 0.95 * 0.15 + 0.1 * (1 - 0.15)

= 0.2275

b) P(has the disease | positive test) = P(positive test | have the disease) * P(have the disease) / P(positive test result)

= 0.95 * 0.15 / 0.2275

= 0.6264

c) P(doesn't have the disease | positive test) = P(positive test | don't have the disease) * P(don't have the disease) / P(positive test result)

= 0.1 * (1 - 0.15) / 0.2275

= 0.3736

milcah answered 1 year ago

A diagnostic test has a probability of 92% of giving a positive result when applied to...

A diagnostic test has a probability of 92% of giving a positive result when applied to a person suffering from a certain disease. The test has a probability of 5% of giving a false positive when applied to a non-sufferer. If 6% of the population suffer from the disease, what is the probability of a positive test result?

A diagnostic test has a probability 0.95 of giving a positive result when applied to a...

A diagnostic test has a probability 0.95 of giving a positive result when applied to a person suffering from a certain disease, and a probability 0.10 of giving a (false) pos- itive when applied to a non-sufferer. It is estimated that 0.5% of the population are sufferers. Suppose that the test is now administered to a person about whom we have no relevant information relating to the disease (apart from the fact that he/she comes from this population). Calculate the...

28. A diagnostic test has a probability 0.95 of giving a positive result when applied to...

28. A diagnostic test has a probability 0.95 of giving a positive result when applied to a person suffering from a certain disease, and a probability 0.10 of giving a (false) positive when applied to a non-sufferer. It is estimated that 0.5 % of the population are sufferers. Suppose that the test is now administered to a person about whom we have no relevant information relating to the disease (apart from the fact that he/she comes from this population). Calculate...

A test for a disease gives a correct positive result with a probability of 0.95 when...

A test for a disease gives a correct positive result with a probability of 0.95 when the disease is present but gives an incorrect positive result (false positive) with a probability of 0.15 when the disease is not present. If 5% of the population has the disease, and Jean tests positive to the test, what is the probability Jean really has the disease?

The sensitivity of a diagnostic test is the probability that a true positive (e.g. someone with...

The sensitivity of a diagnostic test is the probability that a true positive (e.g. someone with the disease under question) is correctly identified as such. The specificity, on the other hand, is the probability that a true negative (e.g. a healthy person) is not reported as a positive. You have a COVID-19 antibody test with specificity α and sensitivity β. There are N people in a particular population, and suppose we already know that n of them have the disease....

A diagnostic test either provides a + result (has the disease) or - result (does not...

A diagnostic test either provides a + result (has the disease) or - result (does not have the disease). 5% of the population has the disease. For a patient with the disease, 75% will test (+)/ 25% will test (-). For a patient that does not have the disease, 15 % will test (+)/ 85% will test (-). Part A) If everyone in the population is tested, what proportion of the test results will be positive? Part B) For a...

71. Use the table below to find the probability. Positive Test Result Negative Test Result Subject...

71. Use the table below to find the probability. Positive Test Result Negative Test Result Subject Uses Drugs 44 (True Positive) 6 (False Negative) Subject is Not a Drug User 90 (False Positive) 860 (True Negative) A. If 2 of the 1000 test subjects are randomly selected, find the probability that both had false positive results. Assume that the 2 selections are made without replacement. (Round to 4 decimals) B. If 3 of the 1000 test subjects are randomly selected,...

BAYES' FORMULA A test for a certain disease gives a positive result 95% of the time...

BAYES' FORMULA A test for a certain disease gives a positive result 95% of the time if the person actually carries the disease. However, the test also gives a positive result 3% of the time when the individual is not carrying the disease. It is known that 10% of the population carries the disease. If a person tests positive, what is the probability that he or she has the disease?

A diagnostic test for a disease has a true positive rate of 98% and a true...

A diagnostic test for a disease has a true positive rate of 98% and a true negative rateof 94%. Suppose the overall disease rate in the population is 1%. That is,•Pr(Positive Test|Patient has Disease) = 0.98,•Pr(Negative Test|Patient does NOT have Disease) = 0.94,•Pr(Patient has Disease) = 0.01.a) What is the probability of a patient without the disease testing positive? b) Find the probability that a patient has the disease given that they tested positive.That is, findPr(Patient has Disease|Positive Test).

Find the probability of a correct result by finding the probability of a true positive or...

Find the probability of a correct result by finding the probability of a true positive or a true negative.

Question