Note: This is using Bayesian statistics (a) Suppose that in a population, the probability of having...
Note: This is using Bayesian statistics
(a) Suppose that in a population, the probability of having a rare disease is 1 in 1000. We use θ to denote the true probability of having the disease. A diagnostic test for this disease has a sensitivity of 99% and a specificity of 95%. A randomly selected person from the population is administered the test and the test and it comes up positive (the test suggests that the person has the disease). What is the probability that the person indeed is suffering from the rare disease?
I know the answer to this question is 1.94%, but have posted this part of the question because the next few parts rely on this part.
(b) Suppose that the person in part (a) had a second test using the same diagnostic tool (a re-test to confirm earlier results). Suppose further that the re-test is negative. What is the updated probability that the person has the disease now that the second test is available?
(c) Consider a different person from the same population as above (part (a)). The person is also tested twice for the presence of the disease. The first test is negative, but the second test is positive. What is the probability that this second person is suffering from the disease and how does this probability compare with the probability you computed in part (b)?
Homework Answers
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Note: This is using Bayesian statistics
(a) Suppose that in a population, the probability of having...
Need details please. Thanks for helping me out ! positive result give that a person 14.A diagnostic test has a probabil...
Need details please. Thanks for helping me out !
positive result give that a person 14.A diagnostic test has a probability of 0.90 of giving a suffering from a certain disease, and a probability of 0.15 of give a (false) positive give that the patient is a non-sufferer. It is estimated that 1% of the population are sufferers of this particular disease. Suppose that the test is now administered to a person about whom we have no relevant information relating...
For a particular disease, the probability of having the disease in a particular population is 0.04....
For a particular disease, the probability of having the disease in a particular population is 0.04. If someone from the population has the disease, the probability that she/he tests positive of this disease is 0.95. If this person does not have the disease, the probability that she/he tests positive is 0.01. What is the probability that a randomly selected person from the population has a positive test result?
2. A rare disease affects 1% of the population. A test has a sensitivity of 98%,...
2. A rare disease affects 1% of the population. A test has a sensitivity of 98%, i.e., it will give a positive result 98% of the time that a person actually has the disease. The same test also has a specificity of 95%, i.e., it will give a negative result 95% of the time when a person does not have the disease. Denote the event that a randomly person has a disease by D, and the event that a randomly...
A bag contains 4 red and 5 green balls. Let X denotes number of red and...
A bag contains 4 red and 5 green balls. Let X denotes number
of red and Y denotes number of green balls in 2 drawn from the bag
by random. Find joint probability distribution, compute E(x), E(Y)
and correlation coefficient. 2. 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 probability0.10 of giving a (false)
positive when applied to a non-sufferer. It is estimated that...
1. A bag contains 4 red and 5 green balls. Let X denotes number of red...
1. A bag contains 4 red and 5 green balls. Let X denotes number of red and Y denotes number of green balls in 2 drawn from the bag by random. Find joint probability distribution, compute E(x), E(Y) and correlation coefficient. 2. 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 probability0.10 of giving a (false) positive when applied to a non-sufferer. It is estimated...
3) A certain blood test for a disease gives a positive result 90% of the time...
3) A certain blood test for a disease gives a positive result 90% of the time among patients having the disease. It also gives a positive result 25% of the time among people who do not have the disease. It is believed that 30% of the population has this disease a) What is the probability that a person with a positive test result indeed has the disease? b) What is the probability that the blood test gives a negative result?...
Only 1 in 1,000 is afflicted with a rare disease for which a diagnostic test has...
Only 1 in 1,000 is afflicted with a rare disease for which a diagnostic test has been developed. When a person has the disease , the test returns a positive result 99% of the time. However, when a person does not have the disease, the test shows a positive result only 2% of the time. When a person's test results are positive, in order to validate the results, a second test is given. The second test has the same accuracy...
3) Suppose the probability of having a disease is .001, and a blood test is 100%...
3) Suppose the probability of having a disease is .001, and a blood test is 100% effective in detecting the disease when the person has the disease. However, the test yields a "false positive" for 1% of healthy persons tested. What is the probability a person has the disease given that his test result is positive? Is the answer approximately a).44 b).01 c).09 d).90
5% of the test population are known to have cancer. The probability of a positive diagnostic...
5% of the test population are known to have cancer. The probability of a positive diagnostic test if the person has cancer is 0.8. In turn, the probability that the diagnostic test will be negative if the person does not have cancer is 0.90. Draw a tree diagram, including all the probabilities with their notation. What is the probability that the test is positive? What is the probability if the test is positive and the person is ill?
The probability of a randomly selected adult having a particular genetic defect is 0.02. Suppose that...
The probability of a randomly selected adult having a particular genetic defect is 0.02. Suppose that a diagnostic test is available and that the probability an adult who has the genetic defect tests positive is 0.97. There is a small probability, 0.01, that a person who does not have this genetic defect will test positive. What is the probability that a randomly selected adult does not have the genetic defect, given the test was positive?
Need details please. Thanks for helping me out !
positive result give that a person 14.A diagnostic test has a probability of 0.90 of giving a suffering from a certain disease, and a probability of 0.15 of give a (false) positive give that the patient is a non-sufferer. It is estimated that 1% of the population are sufferers of this particular disease. Suppose that the test is now administered to a person about whom we have no relevant information relating...
2. A rare disease affects 1% of the population. A test has a sensitivity of 98%, i.e., it will give a positive result 98% of the time that a person actually has the disease. The same test also has a specificity of 95%, i.e., it will give a negative result 95% of the time when a person does not have the disease. Denote the event that a randomly person has a disease by D, and the event that a randomly...
A bag contains 4 red and 5 green balls. Let X denotes number
of red and Y denotes number of green balls in 2 drawn from the bag
by random. Find joint probability distribution, compute E(x), E(Y)
and correlation coefficient. 2. 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 probability0.10 of giving a (false)
positive when applied to a non-sufferer. It is estimated that...
1. A bag contains 4 red and 5 green balls. Let X denotes number of red and Y denotes number of green balls in 2 drawn from the bag by random. Find joint probability distribution, compute E(x), E(Y) and correlation coefficient. 2. 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 probability0.10 of giving a (false) positive when applied to a non-sufferer. It is estimated...
3) A certain blood test for a disease gives a positive result 90% of the time among patients having the disease. It also gives a positive result 25% of the time among people who do not have the disease. It is believed that 30% of the population has this disease a) What is the probability that a person with a positive test result indeed has the disease? b) What is the probability that the blood test gives a negative result?...
3) Suppose the probability of having a disease is .001, and a blood test is 100% effective in detecting the disease when the person has the disease. However, the test yields a "false positive" for 1% of healthy persons tested. What is the probability a person has the disease given that his test result is positive? Is the answer approximately a).44 b).01 c).09 d).90
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