>>52506162 There are three scenarios. In two you picked a goat in the beginning, the host shows you the other goat, so if you switch you get the car. In the third scenario you picked the car, the host shows one of the two goats, if you switch you get a goat. the chance of getting the car when switching is 66.6%.
your chances of having a goat on your first pick are 2/3 compared to 1/3 for a car. the host knows what's behind each door and he has to reveal the second goat switching is the correct way to increase your chance of winning.
>>52506198 Another way of thinking about it is that the initial chance that you pick a goat the first time is 2/3. So it is more likely that you picked a goat in the first place. Since one goat is removed every time. It is more likely that the the other door contains the car, since you are more likely to sit on the goat from the start.
>>52506203 Your theory is flawed anon The car is always is door 1 Scenario 1 You pick 1, host opens 3 switch loses You pick 2, host opens 3 switch wins You pick 3 host opens 2 switch wins This is where your brain ends, BUT You pick 1 host opens 2 switch loses
>>52506252 I didnt pick door 1 twice, i described possible scenarios.
Door 1 has 2 scenarios because the other 2 doors have goats, door 2 has 1 scenario because only door 3 has a goat same applies for door 3. Therefore there are 4 scenarios of which 2 will grant you a car, 50%
>>52506310 The random event of you picking the door has 3 scenarios. The random event of host picking either goat A or goat B has 2 scenarios. Those are different random events and you can't lump them together. You have to use conditional probability instead of just counting all favorable scenarios and dividing by number of all possible scenarios - and if you do that you arrive at 1/3 and 2/3, not 50%.
>>52506101 The host knows the trick and will offer you to switch only if you picked the right one to begin with. So by switching doors you're guaranteed to loose. Unless you actually want the goat, and there is nothing wrong with that. They're wondrous creatures.
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