(February 5, 2009 at 5:57 pm)lilphil1989 Wrote: I understand what you mean.Probability says it will average at 50/50 (or 49/51 according to that font of all knowledge QI!) but what it is saying is that the results will *tend towards* 50/50. The thing is you can only say it's a probability because the chances are that the result will *probably* be 50/50, but there is also a chance that you could get 0/100 or 77/23 (or any other combination).
If we flip 100 coins, probability says there will be 50 heads and 50 tails, but what is the probability of this actually happening in one sample of 100 flips?
Probably not very high! (definitely not 100%, i tried to get a numerical answer but couldnt figure out an expression for the number of possible outcomes that would result in 50 heads, 50 tails, total number of outcomes is 2^100 )
But probability tells you the average in the limit of an infinite number of samples.
A sort of related story...About 20 years ago I was playing Dungeons & Dragons with a group of friends and they had a method for deciding if a character was abidextrous (use both hands equally well). Knowing I was a programmer they assumed I knew maths pretty well (the fools!) and asked me how likely ambidextrous-ness was. I couldn't give them a definitive answer but next day at work I wrote a program to roll virtual dice and keep track of the results.
After leaving it to run for varying numbers of "rolls" (thousands or tens of thousands, this was a long time ago on old computers so it took ages anyway), I saw that the result tended towards a particular level every time and the longer it was left running the closer the fractional part got to a specific value.
My then wife had done maths at university and had covered probability and when I mentioned this she told me the formula to calculate the actual probability of what I was looking for.
Her formula gave me the same number that my program was tending towards.
