5000 persons, 1500 balls, every person get 20 balls, what's the propobility that any one ball (among the 1500 balls) will be got by N persons? (N<=5000)
You're going to have to explain this better. Does each person draw 20 balls, then put them all back for the next person to draw? Or is it that each time a person draws a ball they put it back before the next draw (i.e., its possible for a person to draw the same ball twice)?
Assuming individuals pull 20 balls without replacment, then the probability that any one individual gets the magic ball is 20/1500. The probability that N people out of the 5000 get the magic ball is:
$\displaystyle
p(N) = \left ( \frac {20} {1500} \right )^N \left ( \frac {1480} {1500} \right ) ^{ (5000-N) } C_N ^ {5000-N}
$
Maybe I have not explained my problem clearly,
There are 5000 persons, 1500 balls.
The ball is labeled with seriate number from 1 to 1500. And everyone selects 20 numbers randomly (not picking up balls but recording each number)
What's the propobility that a ball with number X (X is a number between [1,1500]) will be selected by N persons? (N<=5000)
I think the last part of ebaines's answer N!/(5000-N)! should be modified as
5000!/N!
If I am wrong, please help to correct , many thanks.
An easy way to confirm that this isn't right is to test the case where N = 0 (that is, nobody picks the ball with a particular serial number). It's pretty clear that the probability of no one selecting a given ball is(1480/1500)^5000. But your formula gives (1480/1500)^5000 * 5000!