A large industrial firm employs three local hotels to provide overnight accommodations to its clients. From past experience it is known that 20% of clients are assigned rooms at the Ramada Inn, 50% at Sheraton, and 30% at the Lakeview Motor Lodge. If the plumbing is faulty in 5% of rooms at the Ramada Inn, in 4% of the rooms at the Sheraton, and in 8% of the rooms at 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 Lake View Motor Lodge?