The Monty Hall Problem is a widely known brain teaser from which we are able to learn necessary lessons in decision making which are useful basically and specifically for data scientists.
In case you should not acquainted with this problem, prepare to be perplexed 🤯. In case you are, I hope to shine light on facets that you just won’t have considered 💡.
I introduce the issue and solve with three forms of intuitions:
- Common — The guts of this post focuses on applying our common sense to unravel this problem. We’ll explore why it fails us 😕 and what we are able to do to intuitively overcome this to make the answer crystal clear 🤓. We’ll do that through the use of visuals 🎨 , qualitative arguments and a few basic probabilities (not too deep, I promise).
- Bayesian — We are going to briefly discuss the importance of belief propagation.
- Causal — We are going to use a Graph Model to visualise conditions required to make use of the Monty Hall problem in real world settings.
🚨Spoiler alert 🚨 I haven’t been convinced that there are any, however the thought process could be very useful.
I summarise by discussing lessons learnt for higher data decision making.
