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Show written solutions for all of the following problems. Text: Lists, Decisions, and Graphs with an Introduction to Probability, Unit CL: Counting and Listing, Section 4: Probability and Basic Counting. Exercises: 4.1, 4.2, 4.3, 4.4, 4.5, 4.7, 4.9, 4.14 Multiple Choice Questions for Review: 22, 25 Text: Introductory Probability, Chapter 4: Conditional Probability, 4.1: Discrete Conditional Probability. Exercise: 4.1.3, 4.1.4, 4.1.9, 4.1.14, 4.1.18 Exercise The following link will give an example problem (Drug testing) which can be used as a reference to solve the following problem. Here is another link with another example of solving a probability problem (Cat Allergy?) using Bayes' Theorem. Suppose that 8% of the patients tested in a clinic are infected with the flu virus. Also, suppose that when a blood test for the flu virus is given, 95% of the patients infected with the flu virus test positive and 4% of the patients not infected with the flu virus test positive. Find the following probabilities where: F = the patient is infected with the flu virus, E = the patient has tested positive for the flu virus. a) a patient who tested positive for the flu virus with this test is infected with it. b) a patient who tested positive for the flu virus with this test is not infected with it. c) a patient who tested negative for the flu virus with this test is infected with it. d) a patient who tested negative for the flu virus with this test is not infected with it.