Thursday, 20 November 2008

Heads I Win, Tails You Lose!

When we went to St. Andrews we made the mistake of escaping from the cold wind by looking around Waterstones. This is always an expensive mistake! One of the books I bought was How Many Socks Make A Pair? by Rob Eastaway. How Many Socks Make A Pair? aims to make mathematics interesting. Whilst there isn't an equation in sight you will learn about probability theory via the old choosing socks blindly from a draw problem, as well as learning magic and card tricks.

Having previously blogged about the changes to our coins I was particularly interested in a section on coin based probability, particularly the following fact about spinning a penny to determine heads or tails:
What happens if you try and remove the human error by spinning the coin on its axis instead [of flipping it in the air], on a smooth table? It turns out that this is even more biased. Depending on the currency you use, the results can be a long way from 50-50. If you spin an American penny, it has been found to end up showing tails as much as 80 per cent of the time. British pennies are also heavily biased towards tails.
Now given that the tail designs on our coins have changed I was interested to know if this was still true or not. So I conducted my own little experiment. I found two almost mint 2008 pennies; one with the old design and one with the new design. I then spun each coin a hundred times and recorded the outcome. I didn't record spins which didn't get fully up to speed or those that bounced off something else on the table as I felt that these may affect the result.

The first thing to note is that I couldn't replicate the result from the book as the old design penny actually landed 53 to 47 for heads. The new design, however, fell equal with 50 heads and 50 tails.

So what does this all tell us. Firstly the experiment isn't very scientific I'd need a lot more than a hundred spins to show a very small bias. Having said that it looks as if the new design is a fairer coin when spun than the old design.

My Rating: 5 Stars A really interesting book, that makes maths both fun and relevant without resorting to equations.
21 November 2008 at 20:35 , Scriptor Senex said...

I'd already added it to my list of must reads after seeing it in Bryony and Your 'Book of Books'. Anything that makes maths readable has to be good.

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