A large industrial firm uses 3 local motels to provide overnight accommodations

Question

     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 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 person with a room having faulty plumbing was assigned accommodations at the Lakeview Motor Lodge?

Explanation / Answer

Given P(Ramada)=0.2, P(Ramada|Plumbing)=0.05           P(Sheraton)=0.5, P(Sheraton| Plumbing)=0.04           P(Lakeview)=0.3, P(Lakeview|Plumbing)=0.08 The probability that a person with a room having faulty plumbingwas assigned accommodations at the Lakeview Motor Lodge? P(Pluning|Lakeview)=(0.3*0.08)/(0.2*0.05+0.5*0.04+0.3*0.08) =0.44

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