Analysis Probability math problem

An analysis of personal loans at a local bank revealed the following facts: 10% of all personal loans are in default (D), 90% of all personal loans are not in default (D´), 20% of those in default are homeowners (H | D), and 70% of those not in default are homeowners (H | D´). If a personal loan is selected at random, P (D | H) =

a)0.78
b)0.03
c)0.63
d)0.18
e)0.02

P(D & H) = 0.1*0.2= 0.02
P(H) = 0.1*0.2 + 0.9*0.7 = 0.65

P(D | H) = 0.02/0.65 = 0.03 [ b ] <-------------