A large industrial firm uses three 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 Lakeview 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 person with a room having faulty plumbing was assigned accommodations at the Sheraton?