Explanation

This is a Bayes' Theorem application problem. Let's define the events:

• A: Borrower has an agency-secured mortgage loan
• B: Borrower is a millennial

Given probabilities:

• P(A) = 62% = 0.62 (probability of agency-secured loan)
• P(B) = 32% = 0.32 (probability of being millennial)
• P(B|A) = 17% = 0.17 (probability of being millennial given agency-secured loan)

We need to find: P(A|B) = probability of agency-secured loan given millennial status

Using Bayes' Theorem:

$$P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}$$

Calculation:

$$P(A|B) = \frac{0.17 \times 0.62}{0.32} = \frac{0.1054}{0.32} = 0.329375 \approx 0.33$$

Therefore: P(A|B) = 33%

Why other options are incorrect:

• A (17%): This is P(B|A), not P(A|B)
• B (20%): No mathematical basis for this value
• D (52%): This might be confused with P(A) = 62% or some other incorrect calculation

This demonstrates the importance of understanding conditional probability and Bayes' Theorem in risk analysis contexts.