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?

What if we model each coin independently? A coin is either A) red/blue or B) red/red...

We toss one coin, randomly A or B.
After seeing a face of blue, the probability it is B = 0.
After seeing a face of red, the probability it is B = 2/3.

We have 400 coins that each independently have a 2/3 probability of being red, so I guess that there are 267 red/red coins.

I'm not sure how to adjust this after the second trial...

Posted by Caz on 2006-12-23 02:46:10