2.109 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

Step-by-step explanation:

From the given information;

Let R represent Ramadan Inn

S to represent Sheraton; &

L to represent Lakeview Motor

F to represent faulty plumbing

So;

P(R) = 0.2

P(S) = 0.5

P(L) = 0.3

P(F|R) = 0.05

P(F|S) = 0.04

P(F|L) = 0.08

Then; to find the probability there will be a client assigned to the faulty room.

i.e.

P(F) =( P(R) × P(F|R) ) + ( P(S) × P(F|S) ) + ( P(L) × P(F|L) )

P(F) = (0.2 × 0.05) + (0.5 × 0.04) + (0.3 × 0.08)

P(F) = 0.01 + 0.02 + 0.024

P(F) = 0.054

suppose an individual with a room possessing faulty plumbing was given an accomodation at Lakeview Motor

Then:

P(L|F) = P(L) × P(L|F) / P(F)

P(L|F) = 0.3 × 0.08 / 0.054

P(L|F) = 0.4444