SOLUTION: 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

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Question 924028: 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 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?

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
20% Ramada Inn (5% with faulty plumbing)
50% at the Sheraton (4% with faulty plumbing)
30% at the Lakeview Motor (8% with faulty plumbing)
........
P(being assigned a room with faulty plumbing)
P = .20%2A.05+%2B+.50%2A.04+%2B+.30%2A.08 = .054
........
P(Lakeview | faulty plumbing)
P(A|B) = P(A and B)/P(B) = .30%2A.08+%2F+.054