4 ms·
After a lot of brain twisting it sinks in.. and I do probability for living! For doubters: Before the door is opened by the host, you are less likely to have c
by hardik 18y ago
After a lot of brain twisting it sinks in.. and I do probability for living!
For doubters:
Before the door is opened by the host, you are less likely to have chosen the right one(with prob 1/3). Once he opens the door, he eliminates one "bad door". Now, given that you were less likely to have chosen the right one in the first place and one wrong one has been removed, it is highly likely that the residual door is the right one.
- cconstantine 18y agoRight, so the first choice is door 1, and the host reveals that door 3 is a goat. The decision to switch or not is really a decision between door 1 and door 2. At this point isn't your first guess completely irrelevant? I've heard this problem and the reasoning before, and for some reason I can't get myself to believe that switching is better.
- zack 18y agoYou need to switch in order to re-cast your guess.
- deleted 18y ago[deleted]
- emmett 18y agoThere are two possibilities when you pick door 1: either you've picked a door with the prize behind it (33%) or you've picked a door with a goat behind it (67%). Assume you stick. In that case, you have a 33% chance you've picked the right door, as before. Opening another door doesn't change whether you've picked the right door or not originally. Assume you switch. In the case you've picked a door with a goat originally (67%), you will necessarily switch to the door with the prize. In the case you've picked a door with the car originally (33%), you will necessarily switch to a door with a goat. Therefore switching gives you a 67% chance of picking the door with the prize. Another interesting strategy to consider is "randomize" - what if you picked randomly between the two remaining doors? Then you'd have a 50% of getting the prize, since you're selecting randomly between two doors, one of which you know contains the prize.