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?4. {8 points) We are given 5 coins. Two of them have heads on both sides, one has tail on both sides and two are regular fair coins. We pick a coin at madam and ip it. What is the probability that the top side shows head? A1 2 \"coin with two heads\