Two have goats behind them, which one has the car? Photo: Johnson Cameraface@flickr.com

Predictable is the look on people’s faces when I tell them I am reading mathematics. You see, to them mathematics only ever represented an irrepressible demon, something akin to a chore rather than a passion. Mathematics is a labyrinth of challenges and puzzles, dedicated towards achieving the utmost in perfection.

An example of this inexplicable passion concerns the problem known as the Monty Hall Paradox. The problem goes something like this; suppose that you’re on a game show given a choice of three doors. Behind one door is a car, behind the other two, goats. You pick a door, say No. 1; the host, who knows whats behind every door),opens another door, say No. 3, which has a goat. He then offers you the option to switch your choice to door No. 2. Is it in your advantage to switch your choice?

Now, whilst this problem is very interesting mathematically, the response when it was published in Parade magazine in 1990 is equally as interesting. No less than 10000 readers, including nearly 1000 with PhD’s, wrote to the magazine claiming the solution was wrong.

This question often catches people out, as most people assume each remaining door has equal probability, since the player cannot be certain which is the winning door. In actual fact, the player should switch, as doing so doubles the chance of winning from 1/3 to 2/3.  Consider each of the situations when the door you choose contains the car, or the first goat or the second goat respectively (the number you choose is immaterial, since the probabilities remain the same regardless).  If you choose the car (with probability 1/3), the host will reveal the remaining goat, and switching will make you lose. However, if you choose a goat (with probability 2/3), the host MUST reveal the other goat, hence, switching will always get you the car. Switching doors wins the car with a probability of 2/3, and so the player should always switch.

Those writing to Parade were not some students with half an understanding of statistics, they were highly esteemed experts in their field, misunderstanding what is, in effect basic variable change. But so passionate were they about their subject, and what they deemed to be an egregious slight to their profession, that they were willing to risk their reputations on what is only a very simple problem. Such passion for a subject is what to me makes mathematics so interesting. Even in the simplest of situations, people will do whatever it takes to put forward their case. And why would we want it any other way.

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The Badger

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