Simple Probability Problem (I think)

From: Louise (louise_swainston_at_yahoo.co.uk)
Date: 02/08/05 

Date: Tue, 8 Feb 2005 12:44:18 +0000 (UTC)

Hi,
I think this problem is simple, it sounded like it was when I set out
to do it, and now I've just confused myself thinking it through.

I have a population of 1.8 million calls over a fixed time period from
which I take a sample of size 65,000. If a particular type of call A,
occurs 50 times in the time period, what is the probability that I
find at least one call of type A in my sample? And also, if the
probability is very low, what size sample should I be taking in order
to pick up at least one call of type A?

Any help would be most appreciated!
Regards
Louise