Question

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 Ra-
mada 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

Answer 1

= 0.17

Answer 2

From past experience it is known that 20%of the clients are assigned rooms at Ramada Inn,50% at theSheraton, and 30% at the Lakeview Motor Lodge.
and

If the plumbing is faulty in5% of the rooms at Ramada Inn, in 4% of the rooms T Sheraton, andin 8% of the rooms at the Lakeview Motor Lodge,

i.e,
faulty
20% Ramada 5%

50% Sherata 4%

30% Lakeview 8%

Answer 3

(a)
Pr = probability of being assigned to the Ramada and getting a room with faulty plumbing = 0.2 * 0.05 = 0.01
Ps = probability of being assigned to the Sheraton and getting a room with faulty plumbing = 0.5 * 0.04 = 0.02
Pl = probability of being assigned to the Lakeview and getting a room with faulty plumbing = 0.3 * 0.08 = 0.024
The probability that a client will be assigned a room with faulty
plumbing = Pr + Ps + Pl = 0.01 + 0.02 + 0.024 = ?