A Paradox that Fooled 1,000 PhDs!

[ravip]

 

[nausea]

Don't scroll down if you don't want the solution.

 

 

 

 

 

 

 

 

The Monty Hall problem; yeah, it's a good one, very counter-intuitive, many don't get it even after it's explained. A great example of Bayesian probability with prior probabilities playing a major role. Bayesian probability, incidentally, is the reason you think you're coming down with some horrible illness when you look up your symptoms on the Net (been there, done that, got the T-shirt).

 

In very simple terms initially each of the 3 cards, representing 2 goats and a car, has a 1/3 chance of being chosen. So your purely random initial choice would be 2/3 a goat and 1/3 a car. That doesn't change.

 

The guy takes away a goat (and here's the secret - only a goat, not the car).

 

Hey presto, the odds change on the remaining card. Your initial choice remains at 1/3 car, the remaining card has the power both of itself and the card removed - 1/3 car + 1/3 car = 2/3 car. The effect is the same as choosing 2 cards rather than 1. The fact the dealer, rather than you, turns one over is irrelevant as far as the odds are concerned.