The loans department for a large bank has experienced 5% defaults on all personal loans. Of the defaulted loans, 35% were made to men under the age of 30 years. Only 15% of the non-defaulted loans were made to men under the age of 30 years.

a. Using letters of the alphabet and appropriate probability notation, define the two simple events described in this problem and their complements (4 definitions altogether).

b. Draw a probability tree to represent the information given in the question using the letters that you used to define the simple events in part a.

c. What percentage of the banks personal loans have been made to men who are less than 30 years old?

d. A male customer, under the age of 30 years, has just taken out a personal loan. What is the probability he will default on the loan?