LogFAQs > #934396750

LordoftheMorons posted...

There's a definitely possibility that I don't understand your setup correctly, but the best estimate is 51% if I use no extra information (like in reality I would use the fact that I know a normal coin gives a 50% chance and for N flips of a fair coin the standard deviation is sqrt(N/4), so unless there were much more than 2500 flips 1% is a reasonable discrepancy).

The setup is that you don't know the actual probability distribution. You know the outcome of 100 trials and you know that someone had a model before this set of trials that predicted all of them correctly while telling you that they assigned a 51% probability to their being right in each trial. You are being asked to create your model of the situation in light of these facts. Since you have the 51% model you can use it to generate future predictions.

The reasonable conclusion is that the coin has a much higher probability than 51% of turning out the way the 51% model says is 51% likely. Notice how the number 51% is not based in any actual data. It was pulled out of thin air. The person who created that model could have replaced it with 62% or 35% and it wouldn't change the analysis one jot. By the outcome of the 100 trials (you can make it 1 million if you think 100 isn't a big enough sample to you intuitively), you know that these coin flips can be predicted to a high degree of accuracy. Because the 51% model has already done it. Even if it doesn't claim that it should be able to.

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September 1, 2003; November 4, 2007; September 2, 2013
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