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)0.03
B)0.63
C)0.02
D)0.18
E)0.78

Question

Quizplus · Accepted Answer

P (D | H) = P (D ∩ H) / P (H)= P (H | D) * P (D) / P (H)= 0.2 * 0.1 / (0.2 * 0.1 + 0.7 * 0.9)= 0.02 / 0.63= 0.03

An Analysis of Personal Loans at a Local Bank Revealed