This problem was presented to me by Swapna (my wife) on last Friday – I could not work out the right answer even after considerable struggle.
You are participating in a TV show contest. You have reached the last round. If you win this round, you get take home a pure gold brick of 5 KG (5KG = 11.02 lbs); if you lose you have to take away an equivalent quantity of stinking garbage.
Here is the problem in the last round:
There are 3 closed boxes (let us say B1, B2, B3). Inside two of the boxes is garbage. Inside one of the boxes is the gold. You have to open one box and take home whatever is in that box. You decide to open B1. The show-host/ quiz-master asks you to stop, and as a hint opens one of the other two boxes, and inside that box there is garbage. The show-host gives you the option of changing your choice. Would you still go for your original choice or switch to the other unopened box?
Here are some relevant assumptions/ hints/ guidances:
- Most important: you would prefer to take home the gold instead of the garbage :-).
- You will not be able to smell the garbage or gold without opening the boxes, or in any way be able to “know” what is inside the unopened boxes.
- You do not know the show host’s motivation. The show-host may be trying to help you or trick you, or trying to increase hir (his/her) popularity rating, or just following a script. So, do not consider the show host’s motivation in trying to solve the problem (when Swapna presented me the problem, I went on the motivation track, and could not approach it as a problem of probability, even after she told me to ignore the show host’s motivation 🙁 ).
- There is no “trick” in the problem or the solution – so, approach it as a problem of probability/ statistics.
- Do not be lazy and search the internet to find a solution. That is cheating. I have changed some things in the problem so that is not easy to search. However, this is not a test of how quickly and ingeniously you can search the internet.
- You will have to work out the reasons for your choice, not just make a choice. The reasons are more important.
Don’t feel bad if you don’t get the answer right, many renowned statisticians have got it wrong.
The answer is available in another post here.
Please share your views in the “comments” feature available.