Repeating an event probability Q.

kop442000 · #1 $Old$ July 2nd, 2009, 08:52 AM

Hi there.

Imagine I am playing a quiz machine which has a database of only 50 questions.

How many questions would I have to answer on average before I get a repeat.
(I guess I want the modal average?)

Also a rough guide of how to think about this would be great!

Thanks in advance of any replies.

kop442000.

kop442000 · #2 $Old$ July 2nd, 2009, 09:41 AM

ok I have made myself a little excel spreadsheet which I think is right... and now I can see the probability of a repeat after n number of questions.

I make it that when you have seen 9 questions, you have 0.53 probability of having seen it before. Does this sound right?

If so how do I convert this into the number of questions would I have to answer on average before I get a repeat?

Is it just the number at which the probability hits 0.5?

Thanks,
Kop442000.

kop442000 · #3 $Old$ July 2nd, 2009, 11:23 AM

ok I think I have it now.

I calculate that I should expect to see a repeat after 9.54 questions. Feel free to correct or validate.

Thanks.

Plato · #4 $Old$ July 2nd, 2009, 12:48 PM

Quote:

Originally Posted by kop442000 $View Post$

ok I think I have it now.
I calculate that I should expect to see a repeat after 9.54 questions.

That is exactly what I got using $\sum\limits_{j = 1}^{50} {\frac{{P(50,j - 1)(j - 1)}}{{50^j }}j} = {\text{9}}{\text{.54312703934395}}$ .

I was hoping to find the general expectation formula.
Maybe someone else recognizes this.