Finite Mathematics
7th Edition
ISBN: 9781337280426
Author: Stefan Waner, Steven Costenoble
Publisher: Cengage Learning
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Chapter A, Problem 90E
Give the contrapositive and converse of each of the statements in Exercises 89 and 90, phrasing your answers in words.
“If these birds are of a feather, then they flock together.”
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
answer number 6
Chapter A Solutions
Finite Mathematics
Ch. A - Which of Exercises 110 are statements? Comment on...Ch. A - Which of Exercises 110 are statements? Comment on...Ch. A - Prob. 3ECh. A - Prob. 4ECh. A - Prob. 5ECh. A - Prob. 6ECh. A - Prob. 7ECh. A - Prob. 8ECh. A - Prob. 9ECh. A - Prob. 10E
Ch. A - Prob. 11ECh. A - Prob. 12ECh. A - Prob. 13ECh. A - Prob. 14ECh. A - Prob. 15ECh. A - Prob. 16ECh. A - Prob. 17ECh. A - Let p: Willis is a good teacher, q: Carla is a...Ch. A - Prob. 19ECh. A - Prob. 20ECh. A - Let p: Willis is a good teacher, q: Carla is a...Ch. A - Prob. 22ECh. A - Prob. 23ECh. A - Prob. 24ECh. A - Prob. 25ECh. A - Prob. 26ECh. A - Prob. 27ECh. A - Prob. 28ECh. A - Prob. 29ECh. A - Prob. 30ECh. A - Prob. 31ECh. A - Prob. 32ECh. A - Prob. 33ECh. A - Prob. 34ECh. A - Prob. 35ECh. A - Prob. 36ECh. A - Prob. 37ECh. A - Prob. 38ECh. A - Prob. 39ECh. A - Prob. 40ECh. A - Prob. 41ECh. A - Prob. 42ECh. A - Prob. 43ECh. A - Prob. 44ECh. A - Find the truth value of each of the statements in...Ch. A - Prob. 46ECh. A - Prob. 47ECh. A - Prob. 48ECh. A - Prob. 49ECh. A - Prob. 50ECh. A - Prob. 51ECh. A - Prob. 52ECh. A - Prob. 53ECh. A - Prob. 54ECh. A - Prob. 55ECh. A - Prob. 56ECh. A - Prob. 57ECh. A - Prob. 58ECh. A - Prob. 59ECh. A - Prob. 60ECh. A - Prob. 61ECh. A - Construct the truth tables for the statements in...Ch. A - Prob. 63ECh. A - Prob. 64ECh. A - Use truth tables to verify the logical...Ch. A - Prob. 66ECh. A - Prob. 67ECh. A - Prob. 68ECh. A - Prob. 69ECh. A - Prob. 70ECh. A - Prob. 71ECh. A - Use truth tables to verify the logical...Ch. A - Prob. 73ECh. A - Prob. 74ECh. A - Prob. 75ECh. A - Prob. 76ECh. A - Prob. 77ECh. A - Prob. 78ECh. A - Prob. 79ECh. A - Prob. 80ECh. A - Prob. 81ECh. A - Prob. 82ECh. A - Prob. 83ECh. A - Prob. 84ECh. A - In Exercises 8588, use the given logical...Ch. A - In Exercises 8588, use the given logical...Ch. A - Prob. 87ECh. A - Prob. 88ECh. A - Prob. 89ECh. A - Give the contrapositive and converse of each of...Ch. A - Prob. 91ECh. A - Prob. 92ECh. A - Prob. 93ECh. A - Prob. 94ECh. A - Prob. 95ECh. A - Prob. 96ECh. A - Prob. 97ECh. A - Prob. 98ECh. A - Prob. 99ECh. A - Prob. 100ECh. A - Prob. 101ECh. A - In Exercises 93102, write the given argument in...Ch. A - Prob. 103ECh. A - Prob. 104ECh. A - Prob. 105ECh. A - Prob. 106ECh. A - Prob. 107ECh. A - Prob. 108ECh. A - Prob. 109ECh. A - Prob. 110ECh. A - Prob. 111ECh. A - Prob. 112ECh. A - Prob. 113ECh. A - Prob. 114ECh. A - Prob. 115E
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