Houses show that 45% have attached garages 30% have detached garages and 16% have a TV. Also 50% of houses with a TV have an attached garage and 80% of houses with a detached garage do not have a TV.

Question

a) What is the probability that a randomly chosen house has a garage?

Answer: 

b) What is the probability that a house has an attached garage and a home theatre?

Answer: 

c) What is the probability that a house has an attached garage, but no home theatre?

Answer: 

d) What is the probability that a house has a detached garage, but no home theatre?

Answer: 

e) What is the probability that a house has a garage, but no home theatre?

Answer: 

f) What is the probability that a house has a home theatre given it has an attached garage?

Answer: 

Answer 1

a) What is the probability that a randomly chosen house has a garage?

Answer: P(Attached garage) + P(non-attached garage) = 0.45 + 0.30 = 0.75

b) What is the probability that a house has an attached garage and a home theatre?

Answer:  P(attached garage|home theater) * P(home theater) = 0.5 * 0.16 = 0.08

c) What is the probability that a house has an attached garage, but no home theatre?

Answer:  P(attached garage) - P(attached garage & home theatre) = 0.45 - 0.08 = 0.37

d) What is the probability that a house has a detached garage, but no home theatre?

Answer:  P(detached garage) - P(detached garage and home theater) = 0.30 - 0.2 = 0.1

e) What is the probability that a house has a garage, but no home theatre?

Answer: P(garage) - P(garage & no theatre) = 0.75 - (0.37 + 0.1) = 0.28

f) What is the probability that a house has a home theatre given it has an attached garage?

Answer:  P(home theatre and attached garage) * P(attached garage) = 0.08 * 0.45 = 0.036