It is estimated that 1% of the population has a certain genetic defect. A medical test is used to determine if people have this defect and, if a person has this defect, the test will correctly indicate this with probability 90%. However, if a person does not have this defect, the test will still indicate that he or she has the defect with probability 9.6%. If a person tests positive for this defect, what is the probability that the person actually has the defect? Express your answer, rounded to three decimal places, if necessary.

It is estimated that 1% of the population has a certain genetic defect. A medical test is used to determine if people have this defect and, if a person has this defect, the test will correctly indicate this with probability 90%. However, if a person does not have this defect, the test will still indicate that he or she has the defect with probability 9.6%. If a person tests positive for this defect, what is the probability that the person actually has the defect? Express your answer, rounded to three decimal places, if necessary.

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

3. There is a 30% chance of rain today. If it does not rain today, there is a 20% chance of rain tomorrow. If it rains today, there is a 50% chance of rain tomorrow. What is the probability that it rains tomorrow?
There is a 50% chance that a father carries the gene of a certain disease. If he is a carrier, then each of his children has a 50% chance of having the disease independently. If the father is not a carrier, a child will not have the disease. Suppose the father has had three children without the disease. What is the probability the father is a carrier?
Composite blood testing is sometimes used to save costs. A Hepatitis-C composite blood test means that when several blood samples are mixed together and tested for Hepatitis- C. The probability of testing positive for Hepatitis-C in a certain population is 0.490. If 4 bloodsamples are mixed together, what is the probability that composite sample would be positive (in other words, what is the probability that at least one of the people in the group is positive for Hepatitis-C)?
The weather in a particular town in the Pacific northwest is classified as either good, indifferent or bad. If the weather is good on a particular day, the probability it will remain good the next day is only 11%, and there is a 45% chance it will be indifferent. If the weather is indifferent on a particular day, there is a 20% chance it will become good, and a 42% chance it will become bad. If the weather is bad on a particular day, there is a 48% chance it will be bad the next day, and a 21% chance it will become indifferent. Construct the stochastic matrix that models this problem.
A vaccine has a 90% probability of being effective in preventing a certain disease. The probability of getting the disease if a person is not vaccinated is 50%. In a certain geographic region, 25% of the people get vaccinated. If a person is selected at random, what is the probability that he or she will contract the disease?
Suppose 50% of the students in school have a part time job. Among those who have a partime job, 20% of them need to work at least 20 hours per week. If you randomly select a student in school, what’s the probability that the student does not work or works less than 20 hours per week?
Suppose we conduct a study about the effect of a certain trait on the recovery of a person from a certain illness. Let the probability that a person recovers from a certain illness be equal to 0.4 and the probability that a person possesses the trait be equal to 0.3. If getting an illness and possessing the trait are independent events, what is the probability that at least 10 out of the 15 survivors possess the trait?
Records from a medical journal show that 40% of adult males suffer from prostate issues. A random sample of six adult males is selected. What is the probability that exactly four of these adult males suffer from prostate issues? What is the probability that at most one of these adult males suffer from prostate issues?
A drug test facility uses a test that has a 1% false negative rate, and a 2% false positive rate. It is estimated that 4% of the population is taking this drug. If a random person who tested positive is chosen, what is the probability that they are actually taking the drug?
Suppose that historically, 35% of applicants that are offered admittance to Texas Tech actually enroll, while the others take offers somewhere else. If Texas Tech will accept 9000 this coming year, what is the probability that less than 34.1654% will actually enroll?
An assembly line produces a tool. The parts are independently sampled one at a time and tested for compliance. Historically, 0.15 of the parts have been found to be non-compliant. What is the probability that the 6th sampled part will be the 3rd part found to be non-compliant?
It is found that a certain pharmaceutical cures symptoms in 35% adults. If 500 people take the pharmaceutical, what is the probability 200 or more adults have their symptoms cured? What is the expected number of people with symptoms cured?