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
A teacher decides to give a pop quiz one day but all of her students refuse to take the quiz thinking that the teacher will call off the quiz.
She can give only one of these students a detention for skipping the quiz.
All of the students know each other's names and if a student knows he/she is getting a detention they take the quiz.
How can she threaten her students with the single detention so they all take the quiz?
She tells them that she will give the student who skips the quiz whose name comes first alphabetically a detention.
This student won't skip because they know they are getting a detention if they do.
The next person alphabetically will then know that they will get a detention so they won't skip either, and so on.
A king decided to let a prisoner try to escape the prison with his life. The king placed 2 marbles in a jar that was glued to a table. One of the marbles was supposed to be black, and one was supposed to be blue. If the prisoner could pick the blue marble, he would escape the prison with his life. If he picked the black marble, he would be executed. However, the king was very mean, and he wickedly placed 2 black marbles in the jars and no blue marbles. The prisoner witnessed the king only putting 2 black marbles in the jars. If the jar was not see-through and the jar was glued to the table and that the prisoner was mute so he could not say anything, how did he escape with his life?
The prisoner grabbed one of the marbles from the jar and concealed it in his hand. He then swallowed it, and picked up the other marble and showed everyone. The marble was black, and since the other marble was swallowed, it was assumed to be the blue one. So the mean king had to set him free.