2. Consider again the example application of Bayes rule in Section 6.2.1 of Mitchell's textbook; this is the example of a cancer test which we also discussed in the lecture. Consider these two separate scenarios based on the original problem: a. After the first test, the doctor orders a second test for the same patient, and it returns positive again. What are the posterior probabilities of cancer and not cancer following these two tests? Assume that the two tests are independent. b. For a different patient, suppose the doctor has evaluated the patient's symptoms and based on their experience, the doctor believes that there is a 30% chance the patient has cancer. Because of this, they order the cancer test for this patient, and the results come back positive. Using their belief as a prior and the positive test result, calculate the posterior probability that the patient has cancer.

Fig: 1