what is the equation that will tell you the average point in time when
randomly drawn items are picked.  For instance, if you have have a jar
with 100 marbles, one of which is black, on average it will be picked
around number 50, or the middle.  But if you have two black marbles,
the point on average when the second marble will be picked will be
somewhere higher than 50.  That number will go up depending on the
number of black marbles.

Hi trashpad-ga,

Good day and thanks for your question.

Let t=total number of marbles.
let b = total number of black marbles
let P(n) be the pick number where the nth black marble is picked up.

P(n) = (t * n) / (b + 1)

I hope this answered your question. if you have any clarifications,
please don't hesitate to ask.

Thank you for using this service and have a nice day

With regards,
Aditya

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Request for Answer Clarification by trashpad-ga on 07 Mar 2004 13:51 PST

this seems to require a number for the total number of marbles in the
game, and I am not sure that is a factor when what I want to know is,
if the number of black marbles increases, how much smaller is the
remainder of marbles left when the last black marble is drawn, if
randomly done.  It seems to be that if you have ten marbles being
randomly selected that whether it is 100 or 1000 marbles, the
percentage of marbles not yet selected would be the same, making the
inclusion of the total number of marbles irrelevant....what am I
missing?

Hello,

I think it might be (t+1)*n/(b+1). For example, if t=100, b=1, n=1,
this will evaluate to 101/2 = 50.5, which is the average of all #'s 1
through 100.