Question

A firm uses three local hotels to provide accommodations for its clients. From past experience, it is known that 20% of its client are assigned rooms at Hotel A, 45% at Hotel B and 35% at Hotel C. It is also known that the probabilities of Hotel A, Hotel B and Hotel C facing water problems are 0.02, 0.01 and 0.03 respectively.

(a)Draw a tree diagram for the above data

(b)What is the probability that a client will be assigned a room without water problem?

Answer 1

a) Tree diagram

b) P(room without water problems) = $P(AW')+P(BW')+P(CW')$

$=(0.2*0.08)+(0.45*0.09)+(0.35*0.07)$

$=0.016+0.0405+0.0245=0.081$