3 Doors, 2 Goats, 1 Porsche

 

I will take the Porsche, what about you? Fasten your belts, this simple play of probability might end up winning you a brand new Porsche!

Growing up we all experience luck (influenced by probability) all across. From hoping for questions we study to come in the semesters, to hoping for that chick to run besides you in the gym. Consciously or otherwise, we all use a little maths wherever we are.

This one is about demystifying the famous Monty Hall Scenario and come out victorious.

Imagine yourself to be the lucky contestant chosen to play tonight’s game. Now, the rules of the game are pretty simple. There are three doors, behind two are silly goats and the third one veils a shining Porsche. Your goal –To drive away in the car you have always dreamt of!

The show begins. The host shows you the three doors and asks you to pick one. You have nothing to lose. You go ahead and choose the one you hope would lead you to the car. The host, well aware of the content behind each door opens up the one shielding a goat. He now asks if you would like to switch or stay with the door already selected.

But before going forward, I would like you to make this choice. Ready?

Now, most of us would stick with the door we began with, after all everything has been going pretty fine till now. Using the telepathic powers we all possess, we end up staying with the choice already made. The scenario seems to be clear – 2 choices with an “or” option and a 50-50 possibility of winning. But here comes the catch. The possibility of winning doubles if I choose to switch the door?

Yup.  if you switch you will win 2 out of 3 times, and if you stay, the prospect reduces to 1 out of 3.

Overcoming the 50-50 Barrier –

The obvious hurdle we face looking at the two options is to conclude that just like a simple coin, the 50% possibility of landing on either side gets applied here too. This hypothesis is true only when we have no prior details about the options at hand. Absence of information is one aspect, but its presence changes the dynamics of the game totally. What if I tell you the coin has been tossed before, with a head on top? Your perception for head coming up again will no longer be 50%. The same logic allies here.

Don’t believe? Here’s a way to understand it better. Have a close look at the figure below.


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Scenario 1- Stick with the choice made –

There are three situations, one for each possible door with the car being behind Door 1, and the two goats behind Door 2 and Door 3 respectively.

Situation 1: You choose door number 1, the host opens any of the other two and reveals a goat, and because you stay with door number 1. You win the car!

Situation 2: You choose door number 2, the host reveals a goat behind door number 3, and since you are using the stay strategy you stay with door number 2. You get a goat and don’t win the car.

Situation 3: You pick door number 3, the host opens door number 2 to reveal a goat, you stay with door number 3, and you get a goat.

Thus, using the stay strategy, you won the car one out of three times. That means that your chance of winning the car if you adopt to stay is 1/3 or about 33%.

Scenario 2- Switch to a new option–

Again, the position of the car and the goats remain the same. The only difference we will use the Switch strategy.

Situation 1: You choose Door 1, the host opens Door 2 to reveal a goat, you switch to door number 3. You get a goat.

Situation 2: You choose Door 2, Door 2 is unveiled to reveal a goat, now you switch to door number 1. You win the car!

Situation 3: You choose Door 3, the host opens door number 2 to reveal a goat, and switching to door number 1 makes you win the car again!

So, with the switch strategy you won the car 2 out of 3 times. That means your chance of winning the car if you choose to switch doors is 2/3 or about 67%.

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The take away – If you stay, you win once in three go’s. But if you bounce over to a new door, you win twice.  So, next time Mr. Hall asks you to stay or switch, you will know what to do.

You should switch.

But handle the beauty carefully, even a scratch would hurt you as hell!

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