Question 4. [6 Marks] A large industrial firm uses three local motels to provide

Question

Question 4. [6 Marks] A large industrial firm uses three local motels to provide overnight accom modations 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) 3 marks] a client will be assigned a room with faulty plumbing? b) 3 marks] a person with a room having faulty plumbing was assigned accommodations at the Lakeview Motor Lodge?

Explanation / Answer

a) P(faulty plumbing) =P(Rammada Inn and Faulty plumbing+Sheraton and Faulty plumbing+Lakeview Motor Lodge and Faulty plumbing) =0.2*0.05+0.5*0.04+0.3*0.08=0.054

b) P(Lakeview Motor Lodge given Faulty plumbing)

=P(Lakeview Motor Lodge and Faulty plumbing)/P(Faulty plumbing) =0.3*0.08/0.054 =0.4444

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