Puzzles/Decision puzzles/Monty Hall

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Puzzles | Decision puzzles | Monty Hall

Let us assume that you are participating on the show "Let´s make a deal". Monty Hall offers you a choice of three doors. Monty tells you, and you know, that you can trust Monty, that there is one big prize (such as a sports car) behind one of the doors and goats behind the others. He tells you that after you choose a door, he will open a different door than you chose, which contains a goat.

After you have chosen one door, he opens one of the two other doors, which as promised, contains a goat. Now he gives you the chance to switch or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Does it matter whether you switch or stay?