I Recently came across a quote from a book. I like great quotes because they are often inspirational and life changing. The book in question is “How to read a book”, and the quote is:
“Whenever you read something you don’t understand, that’s the only chance you’re ever given to recognize the opportunity to learn something new.”
That quote completely changed the way I now approach every book. To make a long story short, when I now find something that I don’t understand, like a word, or a concept, I read it again or look elsewhere for an explanation. Same thing goes for more complex things I may come across while doing other stuff.
The great thing is that the more you ask questions when you meet something new, the more you’ll develop your intuition, and the faster you’ll learn new material.
There are a least two ways to learn new things when you read a book or magazine. One is to take action, and the other is to understand every part of the text, including those parts that initially sounds difficult. I’m afraid I was missing the second part.
The Monty Hall Problem
This is a nice problem that I decided to include in this article to give you a first scenario where you can apply what you just learned.
The Monty Hall problem is based on the American game show “Let’s make a deal”. The problem is this:
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
Take some time to think about this, do you think you have more chances to win if you switch your door, or it doesn’t matter?
It turns out that the answer is not that simple. Indeed you have more chances to win if you switch the door. I know it may sounds absurd if you never heard about this problem before, so let me try to explain why it’s more convenient to switch the door.
When you choose the door number one, you have 1 chance in 3 that you have chosen the right door. That means that there are 2 chances in 3 that the car is behind one of the other two doors.
At this point the host opens one of the two remaining doors, unveiling a goat inside. Now, you might be temped to think that you have 50% chances that the car is in your door, after all there are only two doors remaining, right? Wrong. The correct answer is that you still have a 1 in 3 chance that your current door is the right one, because when you gave your answer initially, there were three doors to choose from, now two. This means that there are 2 in 3 chances that the car is behind the other door, so it’s more convenient to switch.
If I have not convinced you yet, consider a different scenario. Let’s say there are 1000 doors instead of 3. As before, you choose one door. You have 1 every 1000 chances that you have chosen the correct door. At this point the host looks behind the remaining 999 doors and opens 998 of them, except one. At this point there are only two doors remaining, the one you have chosen before, and another one. The car is either behind your door, or the other one. Now, do you think you have more chances that the car is behind your door, or the other one? Of course now you know there are more chances it’s behind the other one. After all, there are 999 chances every 1000 that the car is behind the other door. The same principle applies with 3 doors as well.
If you still can’t understand what’s going on, don’t be discouraged. This problem is not simple to understand. Go back and read it again. Draw some pictures, search online. It’s when you refuse to give up that you’ll eventually learn something new and develop your intuition.