In the story 'The Lady or the Tiger" which choice must an accused person make?

The accused person has to choose a door.

This kingdom is ruled by a semibarbaric king who believes that fate is the best justice.  He has devised a trial that involves only luck and (in his mind) fate.  If a person is accused of a crime, he is taken to an amphitheater where everyone watches him make a choice. 

Directly opposite him, on the other side of the enclosed space, were two doors, exactly alike...

The accused person has to choose a door.

This kingdom is ruled by a semibarbaric king who believes that fate is the best justice.  He has devised a trial that involves only luck and (in his mind) fate.  If a person is accused of a crime, he is taken to an amphitheater where everyone watches him make a choice. 

Directly opposite him, on the other side of the enclosed space, were two doors, exactly alike and side by side. It was the duty and the privilege of the person on trial to walk directly to these doors and open one of them. 

In the king’s mind, if the person chooses the door with the lady, he is innocent.  If he chooses the door with the tiger, he is guilty.  As you can probably predict, if he chooses the door with the tiger he will be immediately mauled to death.  The lady leads to happily ever after.

But, if the accused person opened the other door, there came forth from it a lady, the most suitable to his years and station that his majesty could select among his fair subjects, and to this lady he was immediately married, as a reward of his innocence. 

It seems perfect to the king, and the people love it.  They come to the spectacle knowing that they will witness either a bloody execution or a wedding celebration.  Either way, they will be entertained. 

The irony is that while the person cannot know what door he will choose, someone else might.  The princess learns which door is which when her lover is accused, and he knows she will know—and signal him.  However, what does she really want?  Does she want him to live, or will she let him die so no one else can have him?  The author does not tell us what happens.  He wants us to follow the clues, or perhaps our interpretation is based on our own feelings about human nature.