“A paradox is an argument that produces an inconsistency, typically within logic or common sense.”-Wikipedia.
Computer scientists study paradoxes to learn about logical inconsistencies because computers (being as stupid as they are!) can not handle them. This is particularly important in the fields of Operating Systems, Artificial Intelligence, Machine Learning, etc. On top of that, paradoxes are extremely fun thought exercises! The unexpected hanging paradox is described as follows:
A judge tells a prisoner that he will be hanged at noon on one weekday in the following week, but the execution will be a surprise to the prisoner.
The Monty Hall problem is one of the most interesting probability puzzles. It is a veridical paradox because the result appears impossible but is demonstrably true. The problem is following:
Suppose you are on a game show. You are asked to choose one of three doors: behind one door is a car and behind the other two are goats. Your goal is to get the car. After you pick a door, the host, who knows what’s behind the doors, opens another door, which has a goat (since the two doors that you did not choose must have a goat). The Monty Hall problem asks, “Should you stick to your original choice or should you choose the remaining unopened door or does it make any difference?”