A large industrial firm uses 3 local motels to provide overnight accommodations for its clients. From past experience it is known that 20% of the clients are assigned rooms at the Ramada Inn, 50% at the Sheraton, and 30% at the Holiday Inn. It is found (a given condition) that plumbing is faulty at 5% of the rooms at the Ramada Inn, 4% of the rooms at the Sheraton, and 8% of the rooms at the Holiday Inn. What is the probability that: (10 pts)

a) A client will be assigned a room with faulty plumbing

b) A person with a room having faulty plumbing was assigned accommodations at the Holiday Inn