Magic Number 1

And now for a bit of maths...
(I continue to be fascinated with the strange results of probability theory..see the Monty Hall problem)

Did you know... if you take any large set of numerical data from randomly selected statistics (importantly, not 'pure' random numbers) then the number 1 will appear as a leading digit about 30% of the time.

The man who first brought this to light was called Dr. Frank Benford, and thus this strange result is called 'Benford's Law'. It is used in accounting to detect fraud, because, for a non-fraudulent set of accounts, running all the figures through a computer will give the result above - the number 1 appears as the leading digit (e.g. 13.00, 1.15, 1602.38) 30% of the time. A result that is significantly different from this and it's time to call in the auditors!

Check out this page for a fuller description. A nice demonstration of why this is the case can be found at the bottom of the page.

The Monty Hall Problem

I've always thought this an interesting problem.. not least for the amount of discussion and disbelief that always entails.

'Suppose you're on a game show and you're given the choice of three doors. Behind one is a car, behind each of the others is a goat. You pick a door, say door A, and the host, who knows what's behind the other doors, opens another door, say B, which has a goat. He then says : "Do you want to switch to door C?" Is it to your advantage to take the switch?'

I'll put the answer in the 1st comment. Keep in mind the solution is somewhat counter-intuitive and has been very controversial in the past!