Solution to the Ruby in the box Puzzle

Answer to the Puzzle of the Day 2099 : Ruby in the Box Riddle
Here is the refresher to the puzzle

Puzzle 2099 - Ruby in the Box Puzzle

Adam kept 3 identical boxes on table. One of them has a ruby in it and 2 are empty. He asks his friend Bob to pick one box randomly. Now after picking one, there are two boxes remaining on the table, one is empty. Adam then removes one empty box from the table. Finally, Bob is allowed to open either the box he picked, or the box lying on the table.

What should he do? 

If you spent enough time thinking about it, Here is the Answer :

This is a classic Monty Hall Problem. The answer is really really counter intuitive. One would think that since one of the empty box is removed, the chance that the remaining have the ruby is 50% each. Hence it doesnt matter. But there lies the twist the chances of having the ruby or not is calculated when it started and not when he removed the empty box.

Lets look at the two scenarios when you swap your box and when you dont.

  1. When you dont swap your box
    Since you are not swapping, the chances remains the same before or after. Initially when you chose the box, the chances of your box having the ruby is 33% (one-third). And chances of it being empty is 66% since 2 out of the 3 are empty.
  2. When you swap your box
    In this case comes two scenarios

    1. If you chose the ruby the first time
      In this case, Adam can only remove the empty box which means the chances of having the empty box is 1 in 3 i.e. 33%. Which means 66% chance of having a Ruby.
    2. If you chose the empty box the first time
      In this case, Adam removes the only remaining empty box, now if you swap – you win for sure.

So for sure, if you swap, the chances of winning are much higher i.e. 66% or higher while if you dont swap it is just 33%. Hence you should always swap!!

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