The story of Monty Hall – and how to improve your chances in life

How many people have heard of Monty Hall?

Well until last week when my 10 year old daughter asked me to help with her homework, I’d never heard of him either. However what happened next really intrigued me… here’s a definition of the Monty Hall Problem from Wikipedia:

The Monty Hall problem is a probability puzzle loosely based on the American television game show Let’s Make a Deal. The name comes from the show’s original host, Monty Hall. The problem is also called the Monty Hall paradox, as it is a veridical paradox in that the result appears absurd but is demonstrably true.

And here’s the problem:

Imagine that the set of Monty Hall’s game show Let’s Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does.

The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn’t hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors.

After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if the contestant stays with their first choice? What if the contestant decides to switch?

Now, like millions of others my instinct… and I have to disclose that I studied statistics as part of my education… was to say the probability is 50:50 and therefore it makes no difference which one of the remaining two doors the contestant chooses next… However, if like me you think this then you’d be wrong:

If the player switches from their original choice then they double the overall probability of winning the car from 1/3 to 2/3.

Amazing isn’t it, and it’s mathematically proven so… sadly, I’m not going to try and explain it here, instead I suggest you look here on wikipedia if you want to understand the science.

So the moral of this story is … always change your mind if a bloke opens a door and there is a goat behind… you might just win a car…. !!!

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