Monty Hall Problem: Explained

The “Monty Hall Problem” is one of the classic mathematical problems which has entertained many and puzzled equivalent number of people. You will agree with me if you are already familiar with it and in case if you are hearing the term ‘Monty Hall Problem’, for the first time, I wouldn’t ask you to shoot yourself. The whole purpose of writing this post is to make more people familiar with this problem. It goes like this…

Imagine you are a participant in a game show. The game is about selecting from three closed doors, behind one is a posh car and behind the other two are goats. Obviously, as a participant, your aim is not to carry home a goat, but the posh car. Upon making your choice, the host, who has prior information about the position of the car, shows you a door, which you haven’t selected and has a goat. Now, he again offers you to make a choice, from the remaining two doors, behind one is a goat and behind other is a car. So, your chances of winning the car shoot up to 50%. As easy as it sounds, right? Now, here kicks in the math which makes this seemingly simple problem complex, easy if you are among those math geeks. Initially, your probability of winning the car was 1/3. That means your probability of losing was 2/3. The moment one of the door behind which there is a goat, is opened, you can increase your chances of winning the car to 2/3, simply by switching your earlier choice. This switch accounts to the variable change, which is like choosing two out of the three doors, initially. Of course a lot of people don’t realize this trick, and fail to take advantage of the second opportunity.

Didn’t I tell you the problem seems easy, but isn’t quite as easy as it seems to be. To make things clear, I created an illustrative picture of the same. So, here let us say, you selected D3. So, the initial probability of winning is 1/3. Once the host shows the goat behind D1, and if you switch to D2 from D1, the combined probability of D1 & D2 still remains 2/3. Finally this switch in choice is what gets you that posh car, behind D2.

Finally, don’t curse me for posting a problem and a solution, none of which I have created. I never claimed that, did I? The only aim to write this article is make more people aware of this classic mathematical problem. Another subtle message which this problem teaches us is, life seldom shows you a small example of the wrong choice that you made. And when it does, switch your choices. It may increase your winning possibility!

PS: If you interested to know more about this problem, please check out the Wikipedia page: Monty Hall Problem

Benefits of Tagging

The worst thing that can happen to someone in love is being more than friend but less than a lover.

~ Alvin Kwardi

These advancing times have made me realize a new trend. The trend of, showing a total resentment towards recognizing a relation as it actually is. The term ‘friend’ has become so generic that when someone introduces you as a friend; it’s not as easy to interpret, as it used to be earlier. Those who feel tags and labels are best suited for products at a super market and should be kept out of relationships, are missing a point. I too do not advocate the practice of putting a tag or label on relationships as we are humans and not products sold at a super market. Having said that I find it a little hypocritical when people fail to call a spade, a spade.

In such a case, what is the possible point am I trying to make? From the past couple of months, I have had enough time to have discussions on various topics with people, I think, whose frequency matches to that of mine. One such discussion made it easy for me to make my point. The second most essential factor after trust, in a strong relation is clear communication. By keeping off from being clear, we would only give a chance for assumptions and doubts to crop up. Make no mistake; the person on the other side can never understand what is going on in your mind on all instances. This is the thumb rule for every relation, and this covers your blood relations too. The point is, don’t put a tag for other’s sake, do it for your own benefit. Recognizing things the way they are is better than subtle hints, which never work, especially in the matters of heart, at least in reality.

Take this for example. If a guy and a girl were, let us say, more than friends and these are the possibilities. 1) The guy is serious and the girl isn’t 2) The girl is serious and the guy isn’t 3) Both the guy and girl are serious 4) Both the guy and the girl are casual about it

In each of these four cases, imagine the down side, if silence did the talking. In the first and the second case, the guy and girl will end up with a broken heart respectively. In the third case, things may work out after a delay. Imagine how much fun the two would have to miss in the fourth case, if you know what I mean. Do you see an upside, without recognizing the relations, the way they are?