Question: A certain college has g good courses and b bad courses, where g and b are positive integers. Alice, who is hoping to find a good course, randomly shops courses one at a time (without replacement) until she finds a good course.
(a) Find the expected number of bad courses that Alice shops before finding a good course (as a simple expression in terms of g and b).
(b) Should the answer to (a) be less than, equal to, or greater than b/g? Explain this using properties of the Geometric distribution.