Let's say I have 20 buckets and each bucket will have exactly 50 balls randomly inserted into them from a group of 1,000 colorless balls. Of the 1,000 balls, I can color as many balls as I want red. How many balls would I have to color red to make sure to some confidence level that each of the 20 buckets has at least one red ball of the 50 random balls placed in it? Could I calculate the number of red balls needed for 70%, 80%, 90% confidence?
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So, if I just looked at a single bucket. The the probability of getting at least one red ball in the bucket would be 1- the probability of getting no red balls in the bucket. The probability of getting no red balls would be the number of combinations of colorless balls minus red balls divided by the combination of all balls. So, for one bucket, I believe it would look something like: 1 - (1000-x Choose 50)/(1000 Choose 50) = .9 (or what ever probability we were going for). Does that look right? If so, how could I expand this for multiple buckets? Thanks. – Max Jun 09 '13 at 14:29