Several questions and please explain the answer.

1. You are going to register a course which could be easy or hard and decided to ask your friends and classmates who have taken the same class before about their experience. All three say that the class is hard. Given that half of all the courses in this program are tough and your classmates are likely to tell you the truth half of the time. What is the probability that the course in question is indeed hard?

2. Your doctor decided to test you for a disease A. Disease A is rare and occurs in one out of 1000 people in the population. But the test result is positive. Given that the test sensitivity is 100% and specificity is 98%, compute the probability of you having disease A.

3. During a different routine doctor visit, your doctor decides to test you for a disease B. Disease B is also rare and occurs in one in ten thousand people in the population. The time the doctor orders two tests. The tests are made by different pharmaceutical companies and each test has a sensitivity of 99.9% and specificity is 99.8%. One test is positive and the other one is negative. Compute the probability of you having disease B.