You are on a gameshow and the host shows you three doors. Behind one door is a suitcase with $1 million in it, and behind the other two doors are sacks of coal. The host tells you to choose a door, and that the prize behind that door will be yours to keep.
You point to one of the three doors. The host says, "Before we open the door you pointed to, I am going to open one of the other doors." He points to one of the other doors, and it swings open, revealing a sack of coal behind it.
"Now I will give you a choice," the host tells you. "You can either stick with the door you originally chose, or you can choose to switch to the other unopened door."
Should you switch doors, stick with your original choice, or does it not matter?
You should switch doors.
There are 3 possibilities for the first door you picked:
You picked the first wrong door - so if you switch, you win
You picked the other wrong door - again, if you switch, you win
You picked the correct door - if you switch, you lose
Each of these cases are equally likely. So if you switch, there is a 2/3 chance that you will win (because there is a 2/3 chance that you are in one of the first two cases listed above), and a 1/3 chance you'll lose. So switching is a good idea.
Another way to look at this is to imagine that you're on a similar game show, except with 100 doors. 99 of those doors have coal behind them, 1 has the money. The host tells you to pick a door, and you point to one, knowing almost certainly that you did not pick the correct one (there's only a 1 in 100 chance). Then the host opens 98 other doors, leave only the door you picked and one other door closed. We know that the host was forced to leave the door with money behind it closed, so it is almost definitely the door we did not pick initially, and we would be wise to switch.
Search: Monty Hall problem
You are standing before two doors. One of the path leads to heaven and the other one leads to hell. There are two guardians, one by each door. You know one of them always tells the truth and the other always lies, but you don’t know who is the honest one and who is the liar. You can only ask one question to one of them in order to find the way to heaven. What is the question?
The question you should ask is "If I ask the other guard about which side leads to heaven, what would he answer?"
It should be fairly easy to see that irrespective of whom do you ask this question, you will always get an answer which leads to hell. So you can chose the other path to continue your journey to heaven.
This idea was famously used in the 1986 film Labyrinth.
Here is the explanation if it is yet not clear.
Let us assume that the left door leads to heaven.
If you ask the guard which speaks truth about which path leads to heaven, as he speaks always the truth, he would say "left". Now that the liar , when he is asked what "the other guard (truth teller) " would answer, he would definitely say "right".
Similarly, if you ask the liar about which path leads to heaven, he would say "right". As the truth teller speaks nothing but the truth, he would say "right" when he is asked what "the other guard( liar ) " would answer. So in any case, you would end up having the path to hell as an answer. So you can chose the other path as a way to heaven.
A girl lives in a house with her parents. There is a cellar door in the house, and her parents warn her to never, ever, open it because she's not ready to see what's behind it.
What is on the other side of the door that her parents don't want her to see?
The girl is locked in the cellar. Her parents are both crazed people who thought the best way to protect their daughter would be by locking her in the cellar since she was born. On the other side of the door is the rest of the house, and the outside world.