Imagine a world where cars have a 2 digit serial number. You want to play a game where you check all the cars in a parking lot to see if there is at least one pair that have the same serial number.

Assumptions:

1. There are 100 possible serial numbers (00, 01, 02, ...,97, 98, 99).
2. All serial number are equally likely (car factories doesn't favor certain serial numbers).
3. The serial numbers are independent (these are just random cars).

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Q: What is the minimum number of cars needed for there to be a 50% (or greater) chance that there is at least 1 duplicated serial number?