Formula for repeats

Stig Holmquist · science forum beginner Joined: 30 Apr 2005 Posts: 48

Regular lotto games have the matrix n/N andn numbers are drawn
without replacement. But consider instead that each number is replaced
before the next is drawn. What then would be the probability of
finding a duplication amongst the n numbers after completing the
drawing?

I generated 50 random numbers with replacement and printed them
in 10 columns and 10 rows and then looked at sets of 5 numbers
at a time going down the columns, because it is ease to spot
duplications at a glance. I found 22 pairs in 100 sets.

I seem to be unable to find a binomial table that allows me to
predict the result I have, so I must assume the problem is
more complex.

What probability formula should I use for the set of 5 out of 50
and what general formula do I need to make a similar
prediction for any "lotto" with replacement, such as 6/49.

Bertil

Duncan Smith · science forum beginner Joined: 29 Apr 2005 Posts: 21

Stig Holmquist wrote:

Google