Probability theory...
You are participating in a TV game. And you are asked to choose one door out of 3. There is a car behind one of the doors, scooters behind the other two.Which door did you choose?
Let's say the first one.
And then the presenter, who knows that behind each of the doors, opens another door - at number 3. And there ... A scooter.
The host asks you: “Does your choice remain outside door number 1?†Or not?
Riddle itself: Should you change your choice in this situation? And why.
Your choice is interesting ... It is not necessary to look in response)))
Answer.
Spoiler Answer to riddle: Yes - worth it. Initially, the probability that the car is behind door number 1 is 33.3%. At the same time, the probability that the car is behind one of the other two is 66.7%. Since the presenter knows that he is behind each of the doors, he naturally opens the door in which the scooter is in order to create intrigue. It does this regardless of which door you choose. Even if you initially chose a scooter, it will not immediately open the door you have chosen, as there is a tough scenario for the TV game.
If you keep your choice, nothing really changes. The probability of 33.3% will remain. However, if you take into account that the presenter opens the scooter in a tough game scenario, then the probability that you will win the car is 66.7% when you change your choice. Probability theory ... And nothing more ...
If you keep your choice, nothing really changes. The probability of 33.3% will remain.
Why? There will be 2 doors left, which means the probability of winning is 50%
-DENIMUSS -
The creators of the TV game do not intend to part with the AAAAA CAR, but they want to stir up the interest of both participants and spectators, so there may be 2 scooters and 1 car, or 3 scooters with equal probability behind three doors (provided that the number of attempts = the number of doors - 1).
However, if the creators of the TV show are not entirely cunning, then in the event that both scooters are found, they undertake to demonstrate the presence of a car behind the remaining out of work door in order to show the fairness of the game in relation to the player.
Much depends on the conditions for submitting the assignment.
1. If the doors are numbered sequentially or not numbered at all, then when choosing the middle door (that is, door number 2), the leader has no choice and, in accordance with the rules of the game, he will have to open the second door. Then the question arises: "If we take into account that" he naturally opens the door in which the scooter is in order to create intrigue, "then the probability of finding a scooter in the middle door is 100%?" If this is the case, then you must initially choose one of the outer doors, without choosing the average one, and then the probability of becoming a happy owner of a four-wheeled friend will be 50%, which, taking into account the rules of the game, when the TV presenter asks the player again in the case of a "scooter"
2. As another option with unnumbered doors, it can be assumed that the player will not choose numbers 1 or 3 as stated in the example, but the "door on the left" or "door on the right", which also leaves no choice for the presenter (arbitrary interpretation of the leading directions to the left "and" right "are not accepted). If we proceed from the already known condition, according to which the presenter creates an intrigue, then at the doors under the conditional (in the absence of valid) numbers 1 and 3 there are scooters with a probability of 100%, and the desired car with equal probability stands in the middle, behind the door with the conditional number 2 In this case, you need to choose the door in the middle.
Probability theories in a television picture? Heh, heh ...
And in general ... not so interesting. Bland and mundane.
SpoilerNight with a star.
Three doors.
They are hiding behind them.
Anna Simenovich.
Nadezhda Babkina.
.... Gennady Zyuganov.
Spoiler Are you ready?
Spoiler
SpoilerProbability theory?
SpoilerMuaghahahahaha !!!
as it was 33 percent, before opening, so 33 will remain after opening, the answer under the spoiler is complete stupidity
BlackNigerSofa
Other cases of development of events are impossible according to the scenario of the game, therefore the probability of winning a car by changing your choice is equal to the ratio of the number of possible cases in which you win a car to the total number of cases.
the probability is 2 (win) / 3 (chance) = 2/3. in percent 66.7. ... When solving this problem, they usually reason something like this: the presenter always removes one losing door in the end, and then the probabilities of a car appearing behind two unopened ones become equal to ½, regardless of the initial choice. But this is not true. The host will certainly suggest the player to change the door, regardless of whether he chose that car or not. This conclusion contradicts the perception of the situation by most people, therefore the described task is called a paradox .. Take three cards, an ace and two deuces, immediately turn one deuce face up - this is an open presenter's window. Now, what is your chance of finding an ace out of two hole cards? Right! 1/2
And if I don't want a car, but I want a scooter. My chance of winning increases significantly))) And applicable to this situation, it becomes equal to 100%
BlackNigerSofa
You have 33% for each option. that is, choosing one of the options. you give a 100% chance of getting 33% for one of the options and 66 for two, and when one is opened there are 2 options 33 for A and 66 for BS, but since there is no B for C 66, this should change the choice ... if not change the choice, then the probability of getting nothing is 66%,
and if you change that - 33%. If someone does not understand why the probability rises to 66%, I will try to slightly change the example:
There are not 3, but 1000 boxes. Of these, you choose one completely random. The "leader" opens the other 998 boxes that are empty. There are 2 boxes left, the one that you chose initially, and the one that the presenter either did not accidentally open, because you chose the correct box initially (chance - 0.1%), or which the host could not open, because there is a prize in it (chance 99.9% ).
I read about it somewhere. In short, the meaning is this: what choice you initially made, stick to that option. The host who opened the other door just trolls you 8)
BlackNigerSofa wrote:
You're just quoting the wiki
I agree. Whatever the probability is 1/2.
7Rain7
This "field of miracles" has long been feces, turned into a stupid show with endless gifts and chatter about anything))
A.Soldier of Light
It was always almost like that, it was just one of the first such shows, a novelty, so to speak. Now there are so many of these talk shows.
Probability theory is random events, here everything is set up ..... merge the author))))
X_ray_83 wrote:
here everything is set up ...
))))))))))))))))))))))))))))))))))
Probabilities - infinity of options at the same time. But the most important thing is that the variant has no beginning and no end! There is no ideal - there is nothing, even hedgehogs know this simple axiom .. The probability that we were born was not very likely, but that we will die is one hundred percent ..
-DENIMUSS -
It would be true if the host himself did not know where the very car is, that is, a random event, but this is nonsense. In the casino, you can also tweak everything. You need 100% confidence that they are telling the truth, and so -20-30% for a divorce, and what 33-50% are you talking about? )))