Empirical Probability

Date: 01/15/99 at 22:27:25
From: Kira Smith
Subject: Statistics, I think

I have been tossing a coin for some minutes, and it has come up heads 
10 times in a row. My friend walks into the room as I prepare to flip 
again. She says that there is a 50-50 chance that the throw will come 
out heads or tails. I say that there is a 1024-to-1 chance that the 
next throw will be a tail and that the chance of throwing another head 
is a longshot. Who is right? If both of us are right, what are we 
measuring? Is it the throw as a function of previous throws, or is it 
a single throw as an independent action unrelated to previous throws?

Date: 01/17/99 at 04:49:55
From: Doctor Pat
Subject: Re: Statistics, I think

Kira,

It seems from your positions that you are both using a different but 
valid approach to statistics. Your friend apparently believes that the 
coin you are flipping is unbiased and is therefore using a theoretical 
approach. He assigns a probability of 1/2 to each outcome and predicts 
that future events are independent of previous outcomes.  

Your response is one of (almost) empirical probability. Having observed 
that the previous results indicate that this coin came up ten heads in 
a row, you should assign the probability of 100% to the probability of 
getting another head (since that is the result of your previous 
results).  

Each of these approaches is used in probability, and each has its 
place; the hard part is figuring out when to use which. 

Empirical results are often used in insurance, for example. Physicists 
also use the empirical results of past experiments to establish the 
theoretical predictions of new experiments.   

For another answer on this topic, see:

  http://mathforum.org/dr.math/problems/dettman12.4.98.html   

- Doctor Pat, The Math Forum
  http://mathforum.org/dr.math/