Sample size, probability

1. Jul 18, 2005

neutrino71

In a set of 400 hats, each hat is represented by one of six colors (brown, pink, red, orange, blue, yellow). You may assume that each color is represented rather equally in the 400 hats.
What is the minimum amount of samples we must take to be likely to have a sample which has a hat of every color?

2. Jul 19, 2005

mathman

"likely" is rather qualitative. If can quantify it, say P>0.9, then an answer can be obtained, although the calculation may be a little messy.

3. Jul 19, 2005

Hurkyl

Staff Emeritus
neutrino: do you have any thoughts about how you might start this problem?

4. Jul 19, 2005

geosonel

what minimum # of hats must be drawn (without replacement) to have probability 1 of having each hat color represented at least once (if each color is "rather equally represented" in the original set of 400 hats)?
(hint: what minimum # must be drawn to use up all colors except yellow, then choose 1 more.)