Suppose a lab is developing a robust new test to look for diabetes in children. If a child actually has diabetes, the probability that the test will be positive is 82%, indicating they have diabetes. If the child does not have diabetes, the probability that the test will be positive is 12%. Suppose 5.4% of all children actually have diabetes. (Round your answer to 3 decimal places, if needed.) (a) What is the probability that a randomly chosen child has diabetes and tested positive? (b) What is the probability that a randomly chosen child tested positive? (c) Given that a test comes up positive, what is the probability the child has diabetes? (d) What is the probability that a randomly chosen child does not have diabetes and tested negative? (e) What is the probability that a randomly chosen child tested negative? (f) Given that a test comes up negative, what is the probability the child does not have diabetes?