1. (3 points) For Problem 4 in Homework 5, given that the coin shows a head after we flip it, what is the probability that it is actually a coin with head on both sides? 2. There is a blood test for some rare disease that occurs with probability 1/10000 for a randomly chosen person. The test is fairly reliable; if you have the disease, it will show "D" (which means positive) with probability 95/100; if you do not have the disease, it will show "D" with probability 5/1000: (a) (4 points) What is the probability that a randomly chosen person gets "D" from the test? (b) (4 points) If a given person gets 'D' from the test, what is the probability that this person has this disease?3. There are a coin with 0 and 1 on each side, a fair tetrahedron die with 0, 0, 0, and 1 one the four sides and a fair die with 0, 1, 1, 2, 2, 3 on the six sides. The coin is unfair: the probability of 1 is p for 0