Probabilities

In this post I explain the way I came to reason about the Monty Hall problem and provide a tool for you to run experiements to see the outcome of different strategies for playing the game. The Monty Hall problem is an interesting probability teaser. The premise is this: suppose you are at a game show with three doors, one of which has a prize. You, as a guest, have two chances of choosing a door to win the prize. The first time you choose, the host eliminates one of the other doors, leaving you with two. So suppose you pick door number 1, the host could then open door number 2 to show you there is nothing behind it, leaving you with 1 and 3. At this point, you get to make your second choice, choosing between 1 and 3. The question of posed in the puzzle is: do you stick with your first choice or switch? ...

It’s Monday morning, and you just got up. You look at the clock, and it tells you the time is now 7.45am. You have a presentation that starts 8.30am, so that gives you exactly 45min to get to the office. Now, you have a few decisions to make here. Breakfast, yes or no? Mode of transportation, bus, metro or biking? Clothing preparation, i.e. throwing on last week’s shirt or ironing new clothes? Each decision will affect your timeline. For instance, breakfast could take up an extra 15 to 20min, between preparation and eating. This will give you less time for other things, and could make you potentially miss the bus. Furthermore, missing the bus could make you late, which would leave a bad impression. On the other hand, arriving hungry could be problematic because you wouldn’t be as sharp as you could be during the presentation. Let’s put aside the fact that you should have just gone to bed and woken up earlier in the first place. The fact is, you now have decisions to make to attain a specific goal, which in this case could be carrying out a good presentation, or just not being late for starters. Each choice leads to other alternatives. Some are expanded, and others dissapear, e.g. missing the bus. As you think about these decisions, you are mentally evaluating your chances of success on the final outcome. ...