Suppose that \( 4 \% \) of a particular population have a particularly nasty disease. There is a test for the disease that correctly identifies those with the disease \( 96 \% \) of the time. However, th this population is given the test as part of a wellness exam. Give answers in decimal form rounded to 4 decimal places as needed. A. Suppose that a random person comes in for a wellness exam and tests positive for the disease. What is the probability that she actually has the disease? \( \square \) B. Suppose that a person comes in for a wellness exam and tests negative. What is the probability that this person does not have the disease? \( \square \) C. What proportion of the total population will test positive? \( \square \) D. What proportion of the total population will not have the disease and will test negative? \( \square \)
Added by Garima
Close
Step 1
The probability that a person who tests positive actually has the disease can be calculated using Bayes' theorem. This theorem states that the probability of event A given event B is equal to the probability of event B given event A times the probability of event Show more…
Show all steps
Your feedback will help us improve your experience
Aishwarya Krishnakumar and 57 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A pharmaceutical firm has discovered a new diagnostic test that has a 90% chance to indicate a positive result for a patient who is infected by a certain disease. If it is tried on 5 infected patients. (a)What is the probability that exactly 4 will be detected? (Round the answer to 4 decimal places) (b)What is the probability that at least two patient will be detected? (Round the answer to 4 decimal places) (c)What is the expected number of detected patients?
Md.Daniyal A.
Suppose that we have a test for a rare disease, and the test is 97 percent accurate. Given a population of 10000 people, of whom 2 percent have the disease, answer the following questions. You may give exact answers, or decimals rounded to three decimal places. How many people have the disease? How many people who have the disease test positive for the disease? How many people do not have the disease? How many people who do not have the disease test positive for the disease? If someone tests positive for the disease, what is the probability that they actually have the disease? If someone tests negative for the disease, what is the probability that they actually do not have the disease?
Aarti K.
The probability that a person has a certain disease is 0.03. Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually present, the probability that the medical diagnostic test will give a positive result (indicating that the disease is present) is 0.88. If the disease is not actually present, the probability of a positive test result (indicating that the disease is present) is 0.01. a. If the medical diagnostic test has given a positive result (indicating that the disease is present), what is the probability that the disease is actually present? b. If the medical diagnostic test has given a negative result (indicating that the disease is not present), what is the probability that the disease is not present? a. The probability is . (Round to three decimal places as needed.)
David N.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Watch the video solution with this free unlock.
EMAIL
PASSWORD