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or calculated probabilities corresponding the disease. from those below. Calculate the at the grandchildren and circle the one to getting a positive test but not having

or calculated probabilities corresponding the disease. from those below. Calculate the at the grandchildren and circle the one to getting a positive test but not having

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section: Chapter Questions
Problem 2P: Family Planning A intend to have two children. What is tie probability that they will have child of...
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6. Conditional probability (tree diagram) [ In class, I demonstrated using a tree diagram to determine conditional probabilities. The example showed how to calculate the probability that one has a particular disease given a positive test for the disease. 1. P(D): the probability of having a disease D 2. the test's true positive rate (called its sensitivity) 3. the test's true negative rate (called it specificity) The tree starts at a root node with two children. One branch is labeled with the probability of having the disease and the other with the probability of not having the disease. The child on the branch with that first probability also has two children. One branch is labeled with the true positive rate and the other the false negative rate. The child of the root on the other branch (labeled with the second probability) has two children. One branch on that is labeled with the true negative rate and the other the other the false positive rate. This yields four grandchildren of the root. The probability of getting a positive test but not have the disease is calculated along the path with the branches "not having the disease" and "false positive rate". Please draw the tree as described above and in class, label the branches appropriately with the values given or calculated from those below. Calculate the probabilities at the grandchildren and circle the one corresponding to getting a positive test but not having the disease. • Probability of having the disease: P(D) = 0.015 • True positive rate (sensitivity) = 0.85 • True negative rate (specificity) = 0.92
Transcribed Image Text:6. Conditional probability (tree diagram) [ In class, I demonstrated using a tree diagram to determine conditional probabilities. The example showed how to calculate the probability that one has a particular disease given a positive test for the disease. 1. P(D): the probability of having a disease D 2. the test's true positive rate (called its sensitivity) 3. the test's true negative rate (called it specificity) The tree starts at a root node with two children. One branch is labeled with the probability of having the disease and the other with the probability of not having the disease. The child on the branch with that first probability also has two children. One branch is labeled with the true positive rate and the other the false negative rate. The child of the root on the other branch (labeled with the second probability) has two children. One branch on that is labeled with the true negative rate and the other the other the false positive rate. This yields four grandchildren of the root. The probability of getting a positive test but not have the disease is calculated along the path with the branches "not having the disease" and "false positive rate". Please draw the tree as described above and in class, label the branches appropriately with the values given or calculated from those below. Calculate the probabilities at the grandchildren and circle the one corresponding to getting a positive test but not having the disease. • Probability of having the disease: P(D) = 0.015 • True positive rate (sensitivity) = 0.85 • True negative rate (specificity) = 0.92
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