Yesterday (or was it last week? 😉 ) I posted a timely thought which explained why history is important. I used an example of flipping an unbiased coin which repeatedly turned up tails, and stated that even though historical performance would suggest another tails on the next flip, the chances of heads showing on the next flip was still 50%.
I think a 50% chance of a heads showing is incorrect. It should be higher!
This is because that there are 2 possible outcomes of a flipped coin, so 50% chance of getting either one of them. The implication then is that with 2 coin flips, we’d expect 1 head and 1 tail. With 4 flips we’d expect 2 heads and 2 tails.
With 100 flips, we’d expect 50 heads and 50 tails.
But who’s to decide the order in which those heads and tails come? Alternate? Or all one and then the other?
So take the example in my original post where 50 flips had given tails. I’d stated a 50% probability of the next flip being heads. But if the probability is 50% for 100 flips, then the probability of the 51st flip being heads is now…100% !!!
So it seems that history is even more important than I had previously thought…although I wonder whether this is because we know something about the future i.e. there will be 100 coin flips and then no more.
But let’s add in a parallel consideration…we’ve considered this particular coin, but shouldn’t we be taking in all coins, and all of their flips, ad infinitum? That would mean we’re back at a 50% chance of a head.
So boundary limits impact the probability; events at all places at all times impact the importance of history and what that history means for the future.
Interesting that although I’m now a little wiser in the future…a little hindsight about foresight would have helped when I first wrote!
Paul
