SOLUTION: We have an urn with 496 marbles of 4 different colors (we don't know the distribution of the colors). If we randomly pick 397 marbles, it is guaranteed that we pick at least one fr

Algebra ->  Permutations -> SOLUTION: We have an urn with 496 marbles of 4 different colors (we don't know the distribution of the colors). If we randomly pick 397 marbles, it is guaranteed that we pick at least one fr      Log On


   

Question 1039407: We have an urn with 496 marbles of 4 different colors (we don't know the distribution of the colors). If we randomly pick 397 marbles, it is guaranteed that we pick at least one from each color. What is the minimum number of marbles we need to pick, so as to have a guaranteed set of 3 colors?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure of your use of the word "guarantee" and what it means.
Do you mean a probability of P=1?
If you have an urn of 496 marbles, you would have to choose all 496 marbles to guarantee (P=1) that you have all 4 colors.
As an example, imagine an urn of 493 red marbles, 1 white, 1 blue, 1 clear.
You could choose 397 red marbles without choosing any other color.
You could even choose all 493 red marbles without choosing any other color.
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.
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The minimum number you would have to choose to guarantee that you have 3 colors in the urn would be 3.
If this isn't what you're looking for, please repost.