a) Assume the probability of being infected with Malaria disease is 0.01. The probability of test positive given that a person is infected with Malaria is 0.95 and the probability of test positive given the person is not infected with Malaria is 0.05. (a) Calculate the probability of test positive. (b) Use Bayes' Rule to calculate the probability of being infected with Malaria given that the test is positive. b) Suppose P(rain today) 2 0.30, P(rain tomorrow) 2 0.60, P(rain today and tomorrow) 2 0.25. Given that it rains today, what is the probability it will rain tomorrow? c) A biased die has the following probabilities of landing on each face: face 1 2 3 4 5 6 P(face) 0.2 0.1 0.1 0.2 0.1 0.3 i) I win if the die shows odd. What is the probability that I win? Compare this to a fair die (i.e., a die with equal probabilities for each face). ii) What is the entropy of this die? Compare this to a fair die