Simulated experience #2

There are 3 doors.

Behind one of them is a Ferrari of your favorite color.

You do not know which door is the winner.You don’t.

But I do!

I ask you to select a door and you make a choice.

Once you choose a door, I eliminate one of the two that you did not select, while making sure that there is NO Ferrari behind the door I eliminate.

Now…

Do you stay with your original choice, or given the option, would you change to the other remaining door?

This is the famous Monty Hall problem. And it confuses a lot of people.

The probabilistic structure, like in the birthday problem, is hard to understand.

Although one might be inclined to think that the odds are 50%-50% at the last stage, it turns out that if you change doors, your chances of getting that Ferrari is 67%, and if you stay, it is only 33%.

There is, of course, an analytic solution to this problem. But why bother? Use simulated experience. Just take 3 playing cards, 2 black and 1 red (Ferrari).

Put them upside down as you make a selection. Then, turn them over, take out a black card out of the ones that you did not select and make a note of the result. You’ll see that when you repeat this procedure over and over again, out of the remaining cards, the red one will mostly be the other card.

Or, play the game HERE.

Simulated experience #1

In a random group of 25 people, what would be the probability that there are 2 people with the same birthday?

This is the famous birthday problem.

We have difficulty in understanding the probabilistic structure of this problem. When I asked this question to 100 university students, the average response I got was “less than 1%.”

The correct answer is actually around 54%!

The analytic solution of the problem is not straightforward. One has to think in terms of combinations. One has to make several complex calculations.

And these don’t come naturally to us.

So what to do?

If you think about it, experiencing frequencies of outcomes would be actually much easier. This would mean going out there and meeting many many groups of 25 people and observing if there are matching birthdays in each group.

Sounds like a hard task to accomplish though.

But wait; we could use simulations.

Check THIS site for instance.

What you do here is to generate 25 birth dates and see if there are two that are the same.

Then reset and meet a new group of 25. Then again. Then again. Then again…

Once you meet a dozen groups like this, you’ll notice that in around half of them, in fact, there is a match.

Consider now the power of simulations and the possibilities of experiencing the outcomes of complex and relevant probabilistic scenarios, such as investment decisions, pension schemes, insurance regimes, with the help of simulations. You would gather much more insight on the problem and possibly make better decisions.

Well… Try with a number larger than 25 this time.

You’ll be surprised.