Recent MLS listings of houses for sale in Edmonton show that 45% have attached garages, 20% have detached garages, and 10% have a home theatre. Additionally, 60% of houses with a home theatre have an attached garage, and 90% of houses with a detached garage do not have a home theatre. (Round your answers to 3 decimal places, if needed.) #8 a) What is the probability that a randomly chosen house has a garage? Answer: b) What is the probability that a house has an attached garage and a home theatre? Answer: c) What is the probability that a house has an attached garage, but no home theatre? Answer: d) What is the probability that a house has a detached garage, but no home theatre? Answer: e) What is the probability that a house has a garage, but no home theatre? Answer: f) What is the probability that a house has a home theatre given it has an attached garage? Answer: 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 85%, indicating they have diabetes. If the child does not have diabetes, the probability that the test will be positive is 12%. Suppose 5.1% of all children actually have diabetes. (Round your answer to 3 decimal places, if needed.) #9 (a) What is the probability that a randomly chosen child has diabetes and tested positive? Answer: (b) What is the probability that a randomly chosen child tested positive? Answer: (c) Given that a test comes up positive, what is the probability the child has diabetes? Answer: (d) What is the probability that a randomly chosen child does not have diabetes and tested negative? Answer: (e) What is the probability that a randomly chosen child tested negative? Answer: (f) Given that a test comes up negative, what is the probability the child does not have diabetes? Answer: