Answer to Question #145637 in Statistics and Probability for qwerty

Question

5. 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 of 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 chance that
Total Probability & Bayes' Rule - Answer must be in PERCENTAGES.

(a) a client will be assigned a room with no faulty plumbing
(b) a person with a room have faulty plumbing was assigned accommodations at the Sheraton

Answer 1

a) if person in motel Ramada he has 95% to a room with no faulty plumbing. if person in motel Sheraton he has 96% to a room with no faulty plumbing. if person in motel Lakeview Motor Lodge he has 95% to a room with no faulty plumbing. Means chance that client will be assigned a room with no faulty plumbing is

$0.2*0.95+0.5*0.96+0.3*0.92=0.946$ or 94.6%

b)S - person was assigned accommodations at the Sheraton, F - a person with a room have faulty plumbing

$P(S|F)=\frac {P(F|S) P(S)} {P(F)}=\frac {0.04*0.5} {1-0.946}=0.37$ or 37%