Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
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Chapter 9.2, Problem 5E
To determine
To graph: A graph with five vertices and as many edges as possible. The name of this graph and how is it denoted.
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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.
Chapter 9 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 9.1 - (Answers can be found in the back of the book.)
1....Ch. 9.1 - (Answers can be found in the back of the book.)
2....Ch. 9.1 - (Answers can be found in the back of the book.)...Ch. 9.1 - (Answers can be found in the back of the book.)...Ch. 9.1 - (Answers can be found in the back of the book.)
5....Ch. 9.1 - Prob. 6TFQCh. 9.1 - Prob. 7TFQCh. 9.1 - Prob. 8TFQCh. 9.1 - Prob. 9TFQCh. 9.1 - Prob. 10TFQ
Ch. 9.1 - 1. [BB](Fictitious) A recently discovered map of...Ch. 9.1 - Prob. 2ECh. 9.1 - 3. One of the owners of the houses in the Three...Ch. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - You and a friend meet three other couples at a...Ch. 9.1 - 8. (a) A graph has six vertices, every two of...Ch. 9.1 - [BB] A graph has six vertices, every two of which...Ch. 9.1 - Prob. 10ECh. 9.1 - Prob. 11ECh. 9.2 - Prob. 1TFQCh. 9.2 - Prob. 2TFQCh. 9.2 - Prob. 3TFQCh. 9.2 - (Answers can be found in the back of the book.) is...Ch. 9.2 - Prob. 5TFQCh. 9.2 - Prob. 6TFQCh. 9.2 - Prob. 7TFQCh. 9.2 - Prob. 8TFQCh. 9.2 - Prob. 9TFQCh. 9.2 - Prob. 10TFQCh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Draw a graph with 64 vertices representing the...Ch. 9.2 - Consider again the graph accompanying Exercise 5...Ch. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - 13. [BB] At most social functions, there is a lot...Ch. 9.2 - Prob. 14ECh. 9.2 - 15. [BB;(a)] for each pair of graphs shown,...Ch. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - For each of the following sequences, determine if...Ch. 9.2 - Prob. 19ECh. 9.2 - [BB] A graph has five vertices of degree 4 and two...Ch. 9.2 - Determine whether each of the graphs in Fig 9.23...Ch. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - 24. [BB](requires calculus) Prove that the number...Ch. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.3 - (Answers can be found in the back of the book.) It...Ch. 9.3 - Prob. 2TFQCh. 9.3 - Prob. 3TFQCh. 9.3 - Prob. 4TFQCh. 9.3 - Prob. 5TFQCh. 9.3 - (Answers can be found in the back of the book.)
6....Ch. 9.3 - (Answers can be found in the back of the book.) If...Ch. 9.3 - Prob. 8TFQCh. 9.3 - Prob. 9TFQCh. 9.3 - Prob. 10TFQCh. 9.3 - [BB] For each of the ten pairs of graphs that can...Ch. 9.3 - Prob. 2ECh. 9.3 - [BB] Draw all nonisomorphic graphs on n =3...Ch. 9.3 - [BB;(b)] for each pair of grpahs shown. If the...Ch. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - [BB] Prove that two graphs that are isomorphic...Ch. 9.3 - Consider the following three graphs. [BB] How many...Ch. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9 - 1. In the Konigsberg Bridge Problem, a tragic fire...Ch. 9 - 2. (a) Draw a configuration of four houses and two...Ch. 9 - 3. Find the solutions, where possible, for the...Ch. 9 - Draw a graph with six vertices at least three of...Ch. 9 - For each of the following sequences, determine if...Ch. 9 - 6. (a) Does there exist a graph with degree...Ch. 9 - Determine whether or not each of the following...Ch. 9 - Answer these questions for each sequence: Does...Ch. 9 - Find a necessary and sufficient condition for the...Ch. 9 - Prob. 10RECh. 9 - Suppose a graph has 49 vertices, each of degree 4...Ch. 9 - Prob. 12RECh. 9 - A graph G has 50 edges, four vertices of degree 2,...Ch. 9 - Prob. 14RECh. 9 - For each pair of graphs shown in fig 9.30 If the...Ch. 9 - Prob. 16RECh. 9 - 17. For each of the following cases, explain why...Ch. 9 - George is examining three graphs G1, G2, G3. He...Ch. 9 - Answer Exercise 18 again, assuming that Georges...Ch. 9 - Prob. 20RE
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