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1. After changing the probability of arriving in the car, the probability of
choosing a sheep for the first time is 2/3, the host The probability of choosing a car the second time after opening the door is 1/2
, so the probability of choosing a car after the first selection of sheep is 2/3 times 1/2 equals 1/3 The probability of choosing a car for
the first time It is 1/3. After the second choice, if you choose not to change, the probability of getting a car is 0
>>>>>>>>>>>>>>. So the total probability of choosing to change is 1/3+0=1/3
2 If the probability of getting a car after
not changing, choose not to change, then the probability of getting a car for the first time is 1/3. Because of not changing, the second choice does not affect the result, 》》》》》》》》》》 is also 1 /3
So the two probabilities are the same,
everyone is struggling with car selection, why not calculate the host selection?
The host's choice is 2 sheep from 3 breeds, which is also random. In fact, it does not affect the result
========================= The
contestants choose Goat No. 1, the host picks Goat No. 2. Converting will win the car.
The contestant picks goat number two, and the host picks goat number one. Converting will win the car.
The contestants pick the car, and the host picks either of the two goats. Conversion will fail.
This guy refers to the first layer that considers the conditional probability. It is good that the probability of picking a sheep is greater than the probability of a car. It seems that the winning chance of switching is greater than not switching, but he did not discuss the second time, the choice of sheep and no sheep. The probability of the car is not equal, how can we discuss it together?
Or do not use probability theory to explain, use popular methods to explain, that is, since the first choice is not a lottery, we can regard it as a trial play, because no matter whether the choice is correct, it does not affect the result, but the host removes an interference item. , a sheep, so we can see that the second choice is the real game, the host removes the distracting item, and the remaining choice has a chance of 1/2. . Swap or not is still equivalence, isn't it?
If you still don't understand? Let me give you an example and see
that there are 2 cards on the table, one is hearts and the other is spades. I will play with you. Whoever draws hearts will win. Then
the one who chooses first or the candidate wins. ? ?
The answer is the same, because the person chosen is random, it does not affect the result, and no one has a 1/2 chance of winning. This is the same as the host's selection. .
Having said so much, I just sighed that the level of college students at MIT is really as good as in the movie. Is China about to surpass the United States?
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