Assume that the last two digits on a car number plate are equally likely to be any of the 100 outcomes 00, 01, ..., 99. Jacques bets Jules at even money, that at least two of the next n cars seen have the same last two digits. What value of n makes this bet fair?
I am pretty sure the answer is 12, as the only way this is fair is when all the number plates are different, which is at 1*0.99*0.98*0.97 etc, and I did this until it got to 0.5, which was after 12 cars.
However, is there a better way of writing this? This is not a very mathematical answer!