I arrived at a probability of 44% or .4444 that a person at the holiday inn will have faulty plumbing. Is this correct? If not, can you please provide step-by-step solution?

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 a person with a room having faulty plumbing was assigned accommodations at the Holiday Inn.