Strategy for them which which has probability of success exceeding 30%


#1

The names of 100 prisoners are placed in 100 wooden boxes, one
name to a box, and the boxes are lined up on a table in a room. One by one, the prisoners are led into the room; each may look in at most 50 boxes, but must leave the room exactly as he found it and is permitted no further communication with the others.
The prisoners have a chance to plot their strategy in advance , and they are going to need it,
because unless every single prisoner finds his own name all will subsequently be executed.
Find a strategy for them which which has probability of success exceeding 30%


#2

Chance for all prisoners surviving can be: 50%

Before the exercise, all prisoners agree that they will each learn the name of the person going in after them. The first prisoner will search the first 50 boxes for his name and for the name of the second person. He has a 50% chance of finding his own name. If he doesn’t find it in the first 50 boxes, everyone dies.

If the first person also finds the name of the person coming after him in the first 50 boxes, he leaves immediately within a pre-agreed time (say, 5 minutes). If he doesn’t, then the next person is in the last 50 boxes, and he waits at least 5 minutes before leaving.

The second person knows whether his name is in the first 50 boxes or the last 50 boxes, based off of whether he had to wait 5 minutes or not. He finds his name, and finds whether the third person is in the first 50 boxes or the last 50 boxes, and waits the 5 minutes if the third person is in the last 50 boxes.

And just repeat…

50% chance the first person finds his own name, and then 100% chance that each subsequent person finds his own name.
Am I correct?


#3

This is one of the famous counter intuitive probabilty problem,where the answer is very counter intuitive.
The full explanation is here-