“Monty Hall problem”的概念、定义、翻译、参考文献-科学参考

Monty Hall problem

Mathematics

A counterintuitive problem in probability; the problem is loosely based on a game show once hosted by Monty Hall. A contestant is presented with three doors, behind one of which is a prize. The contestant chooses a door, and then the host opens a different door to reveal no prize. The contestant now has the chance to change their initial choice for the one remaining door: should they change?

Intuitively it may seem that there is no benefit in changing, as the choice is now just one of two doors. However the chance of the initial choice being right is still the same as it was initially, namely 1 in 3. So there is a 2 in 3 chance that the prize is behind the other door, and so the contestant improves their chance of winning by changing.

Statistics

Monty Hall was host of a TV show in which a contestant was faced by three doors. Behind two of the doors was a booby prize, and behind one was the real prize. The contestant was asked to choose a door. Another door was then opened to reveal a booby prize. The contestant was invited to change to the third door. Intuition suggests that changing would have no effect, yet actually it doubles the chance of winning the real prize.
http://www.shodor.org/interactivate/activities/AdvancedMontyHall/ Applet.

Philosophy

A decision problem associated with the American television game show host Monty Hall. Contestants are shown three closed curtains. Behind one is a prize, behind the other two are lemons. They pick a curtain. Monty Hall (who knows where the prize is) then pulls one of the other curtains, revealing a lemon, and contestants are asked if they would like to switch to the remaining closed curtain, or stay with their original choice. There seems to be no particular reason to switch, yet in fact switching doubles the chances of winning: your chance if you stay with your original curtain is what it always was, namely ⅓; the remaining curtain has a probability of containing the prize of ⅔. The problem was the subject of a minor scandal when several distinguished statisticians failed to see how this could be true. In fact it is true because there is now a significant difference between the curtain originally chosen, and the other one on offer, namely that Monty Hall avoided the second. The logic is more easily seen with a greater number of curtains. If there were 100, and you picked one, then by the time Monty Hall has pulled open 98 with lemons behind them, the chance that the remaining one that he did not pick conceals the prize is 99%. See also three prisoners, paradox of.

单词	Monty Hall problem
释义	Monty Hall problem Mathematics A counterintuitive problem in probability; the problem is loosely based on a game show once hosted by Monty Hall. A contestant is presented with three doors, behind one of which is a prize. The contestant chooses a door, and then the host opens a different door to reveal no prize. The contestant now has the chance to change their initial choice for the one remaining door: should they change? Intuitively it may seem that there is no benefit in changing, as the choice is now just one of two doors. However the chance of the initial choice being right is still the same as it was initially, namely 1 in 3. So there is a 2 in 3 chance that the prize is behind the other door, and so the contestant improves their chance of winning by changing. Statistics Monty Hall was host of a TV show in which a contestant was faced by three doors. Behind two of the doors was a booby prize, and behind one was the real prize. The contestant was asked to choose a door. Another door was then opened to reveal a booby prize. The contestant was invited to change to the third door. Intuition suggests that changing would have no effect, yet actually it doubles the chance of winning the real prize. http://www.shodor.org/interactivate/activities/AdvancedMontyHall/ Applet. Philosophy A decision problem associated with the American television game show host Monty Hall. Contestants are shown three closed curtains. Behind one is a prize, behind the other two are lemons. They pick a curtain. Monty Hall (who knows where the prize is) then pulls one of the other curtains, revealing a lemon, and contestants are asked if they would like to switch to the remaining closed curtain, or stay with their original choice. There seems to be no particular reason to switch, yet in fact switching doubles the chances of winning: your chance if you stay with your original curtain is what it always was, namely ⅓; the remaining curtain has a probability of containing the prize of ⅔. The problem was the subject of a minor scandal when several distinguished statisticians failed to see how this could be true. In fact it is true because there is now a significant difference between the curtain originally chosen, and the other one on offer, namely that Monty Hall avoided the second. The logic is more easily seen with a greater number of curtains. If there were 100, and you picked one, then by the time Monty Hall has pulled open 98 with lemons behind them, the chance that the remaining one that he did not pick conceals the prize is 99%. See also three prisoners, paradox of.
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