The Association of American Universities published a report titled "Looking More Closely at Student Debt." This report explores the issue about the cost of a college education and its impact on student loan debt. Using information from a credit reporting company, the following table provides a percentage distribution for the loan balance of outstanding student loans from individuals with graduate, professional, and undergraduate degree debt.
Loan balance _____________________Percentage
$1-$10,000 ................................ 43.1
$10,001-$25,000 ......................... 29.2
$25,001-$50,000 ......................... 16.5
$50,001-$75,000 ......................... 5.8
$75,001-$100,000 ........................ 2.3
$100,001 or more ......................... 3.1
Suppose that one of these individuals is selected at random.
a. Without using the general addition rule, determine the probability that the individual obtained has a loan balance either between $10,001 and $100,000, inclusive, or at most $75,000.
b. Obtain the probability in part (a) by using the general addition rule.