try to figure out the puzzle for a long time sensational, published 23 years ago in the magazine "Parade Magazine" and has become a kind of echo of the famous American show "Let's Make a Deal" (translated).The fundamentals of the problem was Monty Hall Problem.
try to restore the events described.Imagine yourself then held a party show.You are led to three doors and allow only one point, while cautioning that behind every door hidden prizes.The main prize are the keys to a luxury car that you pick, if you open the "correct" the door for the remaining doors hid consolation prizes - or rather, on the goat.Of course, a consolation prize you will not be happy - you are looking for the top prize.
After much thought, you indecisive point to one of the doors (for example, the first).That is Monty Hall Problem, of course you do not know, so just hope for things that miracles still happen sometimes.
But the leading reason opens the wrong door at which point you choose, and the other (he knows exactly where it is hidden Keys).And he opens the door behind which hid the goat.For example, the third.Drive task easier, providing for selection are now only two doors.Moreover, it offers more time to think and allows to name the other door, if you have any doubts.
Will the chance to pick up the keys, if you change your mind and enter on another door?Think a minute.What will stop?
correct answer is opening another door, you increase the chances of getting the key twice.Doubt?Many doubt.But precisely this is the Monty Hall Problem.
explanation of the paradox in this.Let's say you choose now the first door.Represent door in two values (values).The value of A denote the first (selected just you) door, and the value of B - the remaining doors.The probability of hitting a key A is 1/3, and the possibility of getting the second key value of B is respectively 2/3.Do you agree?Next.If you have the opportunity to open a second and third door, leaning in favor of the values of B, the chances go by car would be twice as much.
consider it more closely.You believe that there is certainly value in goat (at least one) and possibly the keys.Opening one door apart, like, the situation does not change: still remain two possibilities: winning car and win a goat.But focusing on the value of B, the probability of winning, you still will increase to 2/3, as for the quantity A probability is only 1/3.
Another already a schematic, example:
g1 g2 g3 change the selection without changing the selection
to Well Well Well to
Well to Well to Well
g and k to w
where d1 - the door first, D2 - the door the second, D3 - third door, Well - animal (goat), to - keys (machine).
Some do not accept the Monty Hall Problem seriously, arguing that the probability of winning the key is still 50/50 ("either-or").However, reusable verification still confirms the theory has a reasonable right to exist and works in 2/3 of all cases presented.For example, thirty presented opportunities to play you will be able to find the right answer in twenty.And this is quite a high percentage.
And often the Monty Hall Problem used players by betting on roulette, or playing cards.Why did they lose?The answer is obvious: greed kills.Or the excitement.As you wish.After removing the pot, the player is no longer able to stop the raging feelings and makes one more bet, already forgetting about the theory.But the loss has not been canceled.This is the percentage payoff.
Monty Hall Problem proves that after opening the door with a goat game is always profitable to change the initial choice, because the chances of still increasing.Here such here they are, the paradoxes of the theory of probability.
If an explanation remains unclear to you, try to ignore these arguments is the theory of statistical and check (or, if you will, experimentally, in a series of experiments).This math is always fascinating.Good luck!
