Suppose that you are asked to approximate the number of undiscovered bugs that remain in a particular piece of software. You insert $100$ bugs into the software and then have your QA team test the software. In testing, your team discovers $40$ of the bugs that you inserted, along with $120$ bugs that you did not insert.

a$)$ Use these results to estimate the number of undiscovered bugs that remain in the program, assuming that you remove all of the discovered bugs as well as the $60$ remaining bugs that you inserted.

b$)$ Why might this test give inaccurate results?