Empirical ProbabilityDate: 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/ |
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