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 Ra- mada 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:(a) The probability is 0.054(b) The probability is 0.4444Step-by-step explanation:The probability P that a client will be assigned a room with faulty plumbing can be calculate as the sum of three probabilities: P1, P2 and P3P1 is the probability that a client is assigned in Ramada Inn and the plumbing is faulty. This is calculate as:P1 = 20%*5% = 0.01P2 is The probability that a client is assigned in Sheraton and the plumbing is faulty. This is calculate as:P2 = 50%*4% = 0.02P3 is The probability that a client is assigned in Lakeview Motor Lodge and the plumbing is faulty. This is calculate as:P3 = 30%*8% = 0.024Then, the probability P is:P = 0.01 + 0.02 + 0.024 = 0.054For part b, the probability that a person with a room having faulty plumbing was assigned accommodations at the Lakeview Motor Lodge is calculate as a division between P3 and P.Where P3 is the probability that a person was assigned to Lakeview Motor Lodge and has a room with faulty plumbing and P is the probability that a person is going to be assigned a room with faulty plumbing.So, the probability that a person with a room having faulty plumbing was assigned accommodations at the Lakeview Motor Lodge is:Probability = 0.024/0.054 = 0.4444