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 Six hundred coins (Posted on 2006-12-22)
I created six hundred coins. I tell you that each is red on one side, but may be red or blue on the other side. I flip each coin, and show you the resulting colors. You count 400 red and 200 blue. What is your best estimate of the number of coins that are red on both sides?

I flipped all the same coins again, and you count 350 red and 250 blue. How should you modify your estimate?

 See The Solution Submitted by Tristan Rating: 4.5000 (2 votes)

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 re(2): I might think you cheated. | Comment 5 of 12 |
(In reply to re: I might think you cheated. by Federico Kereki)

The reason for finding the cumulative probability of 200 or less blues is that we are flipping well over 400 coins and we have an extreme event: only 200 blue.  I wan't know know how likely it is to have an event such as this occur.

In other words not just 200 blue but also less than 200 blue which is even more extreme.

This is the reasoning behind statistical Hypothesis Tests.

Consider this another way: If you flip a coin 1000 times and get 4999 heads the probability if this happening would be .00798 with a fair coin.  Even though this probability is small it doesn't indicate the coin is not fair.  Instead we look at the probability that the even would be this extreme or more extreme which is .49601 which is not unlikely at all so we don't call the coin unfair.

 Posted by Jer on 2006-12-22 15:03:08

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