Question

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) 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?

Answer 1

Let the probability of a person being assigned a room at the Ramada and that room having faulty plumbing = Pr = 0.2 * 0.05
Let the probability of a person being assigned a room at the Sheraton and that room having faulty plumbing = Ps = 0.5 * 0.04
Let the probability of a person being assigned a room at the Lakeview and that room having faulty plumbing = Pl = 0.3 * 0.08
The above three events are mutually exclusive. Therefore the probability of a person being assigned a room with faulty plumbing is Pr + Ps + Pl = you can calculate