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 Lake view Motor Lodge. If the plumbing is faulty in 5% of the rooms at the Ramada Inn, in 4% of the rooms at the Sheraton, and in 8% of the rooms at the Lakeview Motor Lodge, what, is the probability that

(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 Lakeview Motor Lodge?