A realty company has 100 homes listed for sale. Some of these homes have fireplaces, some have garages, and some have neither. A breakdown is provided in the two-way classification table below.

Question

Fireplace No Fireplace
Garage 50 30
No Garage 10 10

what is the probability that the home selected has a garage, given that it has a fireplace?


b. Are the events Fireplace and Garage independent? Show your proof.

2 marks c. Are the events F and G mutually exclusive? Why?

Answer 1

P(G and F)= P(G) P(F/G) =(80/100)(50/80)=0.8x0.625=0.5. a)They are not independent because the probabilities are not equal. P(F)= 60/100=.6, P(F/G)=60/80=0.75
b)Events F and G can occur together because they are not mutually exclusive.