1. On the second day after buying a used car, you notice that it sometimes makes a grinding noise. Based on this fact and what you know about the car (its age, mileage,etc.), you think it is pretty likely that something is seriously wrong with the car. Before getting any reliable evidence, you estimate that your personal degree of belief in the hypothesis (W) - that something is seriously wrong with the car - is 3/4. You ask your mechanic to run a diagnostic test to see if there in fact is anything seriously wrong with your car. Your mechanic says that the test is 90% reliable - meaning, if there is something wrong with your car, then the test will identify the problem (P) nine times out of ten. If nothing is wrong, then the test will indicatethat there is no problem (~P) nine times out of ten. The test indicates that there is no problem (~P) with your car. Use Bayes' Rule to update your original degree of belief that there is something wrong with your car in light of the test result. In other words, what is the Pr(W|~P)?

2. Despite the negative test result, you still that think it would not be wise to take the risk of driving your car until you have more reliable evidence. So, you ask your mechanic to run the same test again. Once again, the test says that there is no problem (~P). Use Bayes' Rule to revise your updated degree of belief that there is something wrong with your car in light of this new evidence. In other words, what is the Pr(W|~P2)?

Please separate the answers and explanations.