#### jiansonz

##### Diabloii.Net Member

**OT: Probability question that vexes me**

I canÂ´t for the life of me figure this out - how to think to be able to solve it. :tongue:

The problem:

Imagine an urn with 256 scraps of paper in it. Each scrap has a unique number written on it, 1-256.

I draw a scrap and note the number. Then I put the scrap back into the urn, shuffle and draw another number, etc.

I assume that all numbers are equally likely to be drawn and that each 'drawing event' is independent on the others.

The question:

A. How many 'drawing events' do I need to perform until I, with 95% probability, have seen each and every number at least once?

B. Same, but with 99% probability.

(Note: I have

*no*problem solving this for a specific number. (I hope!)

The probability for

*not*drawing the number I am looking for is 255/256 each drawing event. I am looking for a 5% probability to not draw that number in x events.

Thus: (255/256)^x=0.05

x~=765.4

(meaning I need 766 drawing events to get the probabilty over the 95% mark)

But how do I do this for all the numbers at the same time!??!)