If N > 0, you already have at least one of each color. How many do you have to remove before that is no longer true? But seriously, I'm guessing the question you're actually asking is what is the probability p(k) of selecting one of each color when selecting k marbles without replacement, and then, when is p(k) first >= .5? --ms On 2014-06-30 15:50, Bernie Cosell wrote:
It is now clear that I've lost essentially all of my math skills... sigh. My wife asked what seemed to me to be a simple problem but I couldn't see a way to approach it... I kept going down what felt like blind alleys that just got more complicated rather than leading toward a solution:
You have a jar with N *each* of C colors of marbles [that is, you start with the same number of each color, N*C marbles in the jar]. You start removing marbles [without replacement]. What is the expected number of marbles you have to remove to have a 50% chance of having at least one of each color.
Is there some easy/obvious way to approach/analyze this? THANKS!
/Bernie\