Originally posted on 08/16/2012:

Suppose I have 100 quarters in a jar and I wonder if they are unfair in the sense that they have an inherent tendency to land on heads or tails significantly more than 50% of the time. I know the coins are all identical. I hire 100 people to go home with one coin each, and ask them to flip their coin 200 times and record the results. I tell them to come back to me only if they think they have an unfair coin. Each of these 100 people does not know I have hired 99 others to do the same.

Suppose one of the 100 people I hired, let's call him Mr.Ed, comes back to me and tells me his coin landed 130 heads and 70 tails.

1. What is the probability in the head of Mr.Ed that he has an 'unfair' coin?
2. What is the probability in my head that Mr.Ed's coin is unfair?

I am not asking for answers. I want you to think about the answers in terms of relative values not absolute values.

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