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> Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Conti
by tromp 3y ago
> Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Continental; behind the other two, are smelly old goats. The host implores you to pick a door, and you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats.
> “Now,” he says, turning toward you, “do you want to keep door #1, or do you want to switch to door #2?”
There are some implied assumptions. You need to know that the car is randomly placed (or that your door choice was made at random), and that the host always has to show you an empty (ok, goat) door before offering you to switch.
Under those assumptions, the winning odds of the switching strategy equal the odds of your initial pick NOT being the car.
- paulcole 3y ago> You need to know that the car is randomly placed You don't need to know this. > and that the host always has to show you an empty (ok, goat) door before offering you to switch You know this through the line, "Then, the host, who is well-aware of what’s going on behind the scenes." If you can't understand that a game show host won't spoil the game they're hosting, that's on you and a good opportunity to pick up common sense.
- tromp 3y agoIt might be that he only does the reveal-and-switch offer if your original pick was the car.
- paulcole 3y agoIt might be that he only does the reveal-and-switch offer on Fridays as well.
- bemusedthrow75 3y agoWith a following wind.
- bemusedthrow75 3y agoYou don't need to know whether he does or does not do that all the time. Because he did it this time? Amazed this nitpicking is still going on; it's illustrative.
- paulcole 3y agoI once had somebody claim the answer was wrong because we weren't sure if the contestant wanted the car or the goat. This puzzle is like a shibboleth for nitpickers.
- lelanthran 3y ago> This puzzle is like a shibboleth for nitpickers More like a shibboleth for sore losers. Just look at this thread, filled with people who got the wrong answer and want to prove that either the smartest person in the world was wrong or that the question is ambiguous.
- dekhn 3y agoIn many developing countries if you ask somebody whether they want a flush toilet or a mobile phone, most people pick the mobile phone.
- paulcole 3y agoDo you think that given the context of the puzzle – about a US game show, printed in a US paper that the question is being asked in many developing countries? Or are you looking to find fault with something for the sake of finding fault?
- dekhn 3y agoNo, I'm making the pooint that in many parts of the world, a goat is more valuable than a car because of the lack of car infrastructure.
- 3y ago
- AnimalMuppet 3y ago> Under those assumptions, the winning odds of the switching strategy equal the odds of your initial pick NOT being the car. Only if there are three doors - or rather, only if the host eliminates all but two doors, one of which is the one you chose. If there are, say, four doors, and the host eliminates one, your odds of success on switching are not 3/4.