Math problem one: The Time Clock Problem

I was at an orientation meeting for a job which had a situation that lends itself to a math problem. This company uses the last four digits of the employee's Social Security Number to identify the employee on their time clock system. Assuming that the last four digits of the SSN are random (0000 is not valid so valid values are 0001 to 9999) and you have a group of 200 employees, what is the probability that at least two employees have the same last four digits? I will post the answer when I figure it out.

If you know the answer, post a comment or send me an email at bruce.hobbs@gmail.com. Sorry, other than bragging rights, there is no prize for a correct answer.

Updated Aug. 9: A solution to this problem is here. I also changed the problem to add "at least" two employees have the same last four digits.

Updated Aug. 23: I renamed this post from "A math problem for today" to "Math problem one: The Time Clock Problem." Does this mean that there will be additional problems? You bet! But the next one is complicated enough that I'm going to solve it before I post it. That way, I can post the solution the next day. The common theme of these problems: These are problems that occur in real life.