Mia and Nia are two roommates who live in the room directly above yours. They aren't friends, so whether each is in their room is independent of the other being in the room.

(a) On Saturday night Mia goes out with probability 3/4 and Nia goes out with a probability 2/3. What is the probability that exactly one of the roommates is in their room on Saturday night?

(b) On Sunday night the probability that exactly one roommate is in their room is 0.5 and the probability that both are in is 0.1. When one roommate is in, she stomps loudly on the floor at an average rate of 3 stomps per hour. When both are in, they stomp at a combined average rate of 6 stomps per hour. Assume the number of stomps per hour are Poisson-distributed. You listen for an hour on Sunday night and hear no stomps coming from upstairs. Given this information, what is the probability that exactly one of the roommates is in their room on Sunday night?Give your answer to 4 decimal places.