Problem 1. People in the country are dealing with a new virus with infection rate of 0.1%, i.e., on average 1 out of 1,000 people are infected daily. There is a test to check whether a person has the disease. The test is not absolutely accurate. In particular, we know that the probability that the test result is positive (suggesting the person has the disease) given that the person does not have the disease is 5 percent (false positive); the probability that the test result is negative (suggesting the person does not have the disease), given that the person has the disease, is 10 percent (false negative). A randomly selected person is tested positive. What is the probability that the person has the disease? Problem 2. A small community consists of three high schools: Bishop's School, Yeshiva School, and La Jolla School, with enrollment of 500, 300, and 200 students, respectively. On a given day, the percentage of students absent at Bishop's School, Yeshiva School, and La Jolla School are 4%, 2%, and 3%, respectively. Find the following probabilities if a student is uniformly chosen at random from the community. (a) Probability that the student is absent (b) Conditional probability that the student is from La Jolla School, given that the student is absent (c) Conditional probability that the student is from Yeshiva School, given that the student is present