At some point in your life, you probably have heard about monty hall’s problem. Here’s a link to the wiki page about it. Let me summarize the problem. You are in a game show with 3 doors. Behind one door is an awesome car, and the other two doors have goats behind. Now you pick a door, and the host reveals another door with a goat. The question now becomes, should you switch the door, or stick with your original choice? What is mind boggling about it is the fact that switching will allow you to have \(\frac{2}{3}\) probability to win the grand prize. This is not another post about explaining why switching will allow you to win, there are plenty of excellent resources on the net and there is no point of reinventing the wheel. This is a post about given this result, can we use this fact to do something useful?

Suppose you are writing a multiple choice exam that is made of 3 option multiple choice questions. If there is a question that you don’t know how to answer, the probability of getting it right is \(\frac{1}{3}\). So pretend to be a contestant and circle a random choice first. But don’t give up yet. What if, at this point, you pretend to be the host. So that out of the other two options, you are able to pick the other goat. After pretending to be host, by pretending to be the contentant and switch the door, you can get the answer right \(\frac{2}{3}\) of the time! Realistically you won’t be able to boost your probability up to \(\frac{2}{3}\) because I’m assuming that your ability as a host to eliminate a bad answer given 2 answers is 100%. However, any attempt to eliminate an answer will improve your odds getting a question right! So my proposed strategy for guessing a 3 choice multiple choice question is as follows:

  1. never choose a.
  2. if not b, choose c, else choose b.

An even better one, if you have a fancy calculator to generate random numbers:

  1. randomly generate a number out of 1 to 3, that number is not the answer.
  2. eliminate one, and choose the other.

You may ask, well this is not practical, because most multiple choice questions have 4 or 5 answers. Well now that you know how 3 answered multiple choice question works, it is time for you, the reader to figure out how to improve the odds of answering those questions correctly :)