1. (apply total probability and Bayes’ rules) A large industrial firm uses three

Question

1. (apply total probability and Bayes’ rules) A large industrial firm uses three local motels to provide overnight accommodations for its clients. From past experience it is known that 22% of the clients are assigned rooms at the Ramada Inn, 50% at the Sheraton, and 28% 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? 

Explanation / Answer

(a) Pr(A client is assigned for faulty plumbing) = Pr(Ramada Inn) * Pr(Ramada inn faulty plumbing) + Pr(Sheraton) * Pr(Sheraton faulty plumbing) + Pr(Lakeview Motor Lodge) * Pr(Lakeview Motor Lodge faulty plumbing)

= 0.22 * 0.05 + 0.50 * 0.04 + 0.28 * 0.08 = 0.0534

(b) Here,

Pr(Lakeview motor lodge accomodoated l Faulty plumbing) = 0.28 * 0.08/ (0.22 * 0.05 + 0.50 * 0.04 + 0.28 * 0.08) = 0.4195 or 0.42

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