Three Doors?

Question

There are three doors. Behind one door is a prize and behind the other two doors is nothing. You pick one door which remains closed, and one of the other two doors, always one with nothing behind it, is opened. You will then get another option to stay with the door you orginally picked or change to the other door. After you make your decision, the door is open to see if you won the prize. Question: Why is it mathematically better to switch doors than to stay with your original decision ?

Answer 1

I'm sure u have worked out the possibilities and also realised by switching, your chance is increased. I'd just answer the "why". Information.

The essence of probability is, making decision based on incomplete information. when u have to guess head and tail, u r given incomplete information of "it's either head or tail". If i give u additional information "It's not head", u will have additional information, and in this case, u can make perfect decision (a). If i tell u, "the coin is biased with higher chance of getting a tail" I gave u additional information as well. What i m doing here is simply to provide u with more information and this affect your opinion/assessment of the probability of event.

By opening one door which definitely has no prize behind it, I'm essentially giving u information. I am telling u, "It is not behind this door"(analogous to (a)). The action of opening the door is non random and hence it contains information.



Imagine this:
When 1 out of 3 times, your first choice is right, the door opener would not need to choose and just has to open any one of the remaining 2 doors. His action does not help u in anyway.

When 2 times out of 3, your choice was wrong, the organiser would CHOOSE the prized door and NOT open it. he tells u which door has the prize by NOT opening that door.

so, although not definite, not 100%, but 2 times out of 3 times, the door opener is actually telling u which door has the prize! If u "listen" to him, 2 times out of 3 times, u will get the prize. This is definitely better than u blindly guessing where u only get 1 times right out of 3 times.

Answer 2

B/c you originally had less of a chance to pick the door with the prize ( 1 out of 3) Now you have a better chance seeing that it is only 2 doors ( 50/50 ). But it does not matter if you pick the other a stay the same. Mathmatically you have a better chance from 2 doors over 3 doors.

Answer 3

Your odds increase from 1/3 to 2/3 when you switch.

Obviously when you start you have a 1/3 chance of picking the prize. Stated another way, there is a 2/3 chance that the prize is in the two that you didn't pick.

Essentially the host is letting you switch your choice to the other *two* doors. Now he eliminates one as empty, but that means if the prize was originally behind one of those two doors, you'll get it. This is equivalent to just saying, "do you want what is behind these two doors (where this one is obviously empty)".

So your odds increase from 1/3 to 2/3 and you should always switch.

Answer 4

This is called 'Monty Hall's Dilemma'. It's discussed in great detail on the 'Marilyn is Wrong!' website (http://www.wiskit.com/marilyn/gameshow.html). The Marilyn referred to is Marilyn vos Savant, the woman who holds the world record for the highest score on an IQ test. She writes a column for Parade magazine.

You originally had a 1/3 chance of being right. You had a 2/3 chance of being wrong. The game show host already knows which door hides the prize and ALWAYS opens a non-winning door. That means the 2/3 chance you were originally wrong has been concentrated into the remaining door.

Switch doors! You have twice as much chance of winning by switching as you do by sticking with your original choice.

Answer 5

You have a probability of 1/3 with your first pick.
Since there is only one door left, and and probabilities must add to 1, the probability of being behind the unopened door must be 2/3! You should switch.

You people who adamently claim there is no difference should not answer questions when you know nothing about the subject.

Answer 6

Call the three doors A, B, and X, with the prize behind X.

One third of the time you will pick A. Door B will be opened, and by switching you will win.

One third of the time you will pick B. Door A will be opened, and by switching you will win.

One third of the time you will pick X. Either A or B will be opened, and by switching you will lose.

Thus by switching you will win 2/3 of the time, and by sticking you will win 1/3 of the time.

Answer 7

You have a 1/3 chance to get the price

Answer 8

Probability increases.

Answer 9

I really dont think its "mathmatically better" to switch, theres no theroy or equation about that type of probability

Answer 10

No, no longer quite, its slightly garbage seeing as devil would teach the guy which of the rooms at the same time as they're at their standard ranges... Josh CANDYMAN the **** skill $hit ! they're upto their necks in shiyt!~!!~!