A bank faces two types of borrowers, type A and B. Both want a $225 loan. Type A repays the loan 100% of the time and type B only repays with probability 0.66. The bank doesn't observe type, but believes fraction x is type A. What does x need to be so that the bank can afford a pooling interest rate of 25%?  A) 0.51 B) 0.47 C) 0.41 D) 0.36

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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A bank faces two types of borrowers, type A and B. Both want a $225 loan. Type A repays the loan 100% of the time and type B only repays with probability 0.66. The bank doesn't observe type, but believes fraction x is type A. What does x need to be so that the bank can afford a pooling interest rate of 25%? 

A) 0.51

B) 0.47

C) 0.41

D) 0.36

 

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