A single bank is considering two options: First, it can make a $$200,000$ mortgage loan for a customer with a $10$ percent probability of default, or second, it can buy a $$200,000$ security representing a bundle of $100$ mortgage loans, which break down as shown in the table below.

You can calculate the weighted risk for each firm category by multiplying the percentage of loans represented $($for example, the first tier includes $40$ loans, which is $\frac{40}{100}=40\%$ of the total$)$ times the probability of default on loans of that category.

Instructions: Round your answers to three decimal places.

a$.$ Calculate the weighted risk for each type of loan, then add together the weighted risks to come up with an overall expected default risk for this financial investment.

$\backslash$table$[[$Number of Loans,$\backslash$table$[[$Probability of$],[$Default $(\%)]],$Weighted Risk$],[40,3,9],[15,11,9],[15,1\mathrm{.}6,9],[30,\frac{?}{\text{b}\text{a}\text{r}}(5),9]]$

Adding together the weighted risks, the expected default risk for the security is: $\%.$

b$.$ If the bank is willing to take on only projects for which the default risk is $6\%$ or less, it should choose the $($Click to select$).$