1. Chad, Bayes, Car, and Vacation. Chad is taking a Bayesian Analysis course. He believes he will get an A with probability 0.7. At the end of semester he will get a car as a present form his rich uncle depending on his class performance. For getting an A in the course he will get a car with probability 0.8, for anything less than A, he will get a car with probability of 0.1. If Chad gets a car, he would travel to Cocoa Beach with probability 0.7. or stay on campus with probability 0.3. If he does not get a car, these two probabilities are 0.2 and 0.8, respectively. TOLL EAST 528 Cocoa Kennedy Space Ctr Figure 1: Chad on the road After the semester was over you learn that Chad is in Cocoa Beach. What is the proba- bility that he got a car? Hint: You can solve this problem by any of the 3 ways: (i) use of WinBUGS or Open- BUGS, (ii) direct simulation using Octave/MATLAB, R, or Python, and (iii) exact calcula- tion