Throwing darts at Monte Carlo

Kailash Awati writes the blog Eight to Late; in a recent post, he makes a humorous but quite informative explanation of the Monte Carlo process by analogy with a drunk throwing darts at a target.  Entitled "A drunkard's dartboard: an intuitive explanation of Monte Carlo methods", he addresses a paradox that may have occurred to many, to wit:

.... that one can get accurate answers via random numbers. 

Permit me to comment:
'accurate' only in the sense that a Monte Carlo will provide distribution of possible outcomes [answers] weighted by the probability [strictly: the probability density.  That is, probability per unit of output], and the accuracy of this range of answers is highly dependent on the inputs provided to the simulation tool.  So, it's still a matter of guarding against "garbage in/garbage out"

Nevertheless, in his clever post, Awati uses simple geometric shapes to demonstrate the answer to that paradox. In the end, I was convinced!

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