Is there a general equation for an inverse hypergeometric distribution? Greetings, I'm making a statistical calculator for game analysis, and have an interesting problem. Here is a specific example: I have a sack of 100 balls and are going to take 10 out of it randomly. I want to find 3 or more blue balls 85% of the time. How many blue balls must I have in the sack to have this probability of success? X = 100 Y = ? K = 10 R = 85% N = 3 In general terms: To achieve at least N successes R percent of the time in a sample size of K, how many items Y in a set of X items must be successes? I arrived at a general equation by my own calculations to find N given R, but it indicates I need about 43 blue balls get achieve my desired 85% chance. However, using a standard cumulative hypergeometric distribution to find R given N, I calculate that using 43 balls will give me a 88.9% chance of success. Consequently, I know my method is in error, and am hoping I can have some help in figuring a general equation for this problem. It would seem what I am seeking is an inverse hypergemoetric distribution. The equations and work so far can be seen in the google docs spreadsheet I have created for them http://spreadsheets.google.com/ccc?key=0AnPw5qvi2hRrdHoweklSQnBuVW9NbVFIUENpYmUyV3c&hl=en". You can see my work on the Chance to Draw Stats and Probability tabs. Any input would be appreciated.