**Reworking Probability Problem with Tree Diagrams**To tackle problem 18 from section 3.3 of your textbook, you will fill in missing probabilities using a tree diagram. Start by constructing figure 3.11 where the first outcome is one of (A, B, C) and the second outcome in each case is one of (1, 2, 3). Note that outcome C is limited to options 1 or 2.Apply these probabilities:- \( Pr[A1] = \frac{1}{12} \)- \( Pr[2|A] = \frac{1}{3} \)- \( Pr[A2] = \frac{1}{12} \)- \( Pr[A3] = \frac{1}{12} \)- \( Pr[B1] = \frac{1}{12} \)- \( Pr[2|B] = \frac{1}{3} \)- \( Pr[B3] = \frac{1}{12} \)- \( Pr[C1] = \frac{1}{12} \)- \( Pr[C2] = \frac{1}{8} \)**Find the following missing probabilities:**1. \( Pr[A] = \) [ ]2. \( Pr[1|A] = \) [ ]3. \( Pr[2|A] = \) [ ]4. \( Pr[B] = \) [ ]**Detailed Explanation of Diagrams:**The problem involves using a three-layer tree diagram. Begin at a root, branching into outcomes A, B, and C. From each of those branches, additional branches represent values 1, 2, or 3 based on the given probabilities. This exercise involves not just computation, but a strategic visualization of probabilities through a tree diagram, providing a solid foundation for understanding complex probability scenarios. The image contains five mathematical probability expressions, each followed by an empty input box for entering answers. Here are the expressions provided:1. \( \text{(5) } Pr[1|B] = \) 2. \( \text{(6) } Pr[3|B] = \)3. \( \text{(7) } Pr[B2] = \)4. \( \text{(8) } Pr[C] = \)5. \( \text{(9) } Pr[1|C] = \)6. \( \text{(10) } Pr[2|C] = \)All expressions have empty boxes next to them, indicating where answers can be filled in. Each box also features a grid icon, suggesting perhaps a calculator or reference tool is available to assist with the input.

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Answered: Rework problem 18 from section 3.3 of…

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...

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Anthony has just received Covid-19 test results from a patient named Melania. The accuracy of the test is as follows: the probability the test will be positive if Melania has Covid-19 is p, and the probability the test will be positive if Melania does not have Covid-19 is q. The proportion of the population that has Covid-19 is 7. The test comes back positive. Anthony has no information about Melania's symptoms. (For reasons he does not understand.) Problem 3c What value of y would result in the simple model of base-rate neglect we learned in class? 67 O 33 O 25 Question 24 Problem 3d If p = .95, q = .05, and r = .1, what must be the value of y if Anthony believes that the probability Melania has Covid-19 is .9? O 3.214 O 5 O 1.05 O 3.57
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Anthony has just received Covid-19 test results from a patient named Melania. The accuracy of the test is as follows: the probability the test will be positive if Melania has Covid-19 is p, and the probability the test will be positive if Melania does not have Covid-19 is q. The proportion of the population that has Covid-19 is 7. The test comes back positive. Anthony has no information about Melania's symptoms. (For reasons he does not understand.) wiet value of ya would result in the simple model of base-rate neglect we learned in class? 67 O 33 25 Problem If p = .95, q = .05, and a = .1, what must be the value of y if Anthony believes that the probability Melania has Covid-19 is .9? 3.214 O 1.05 O 3.57
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