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Determining the result of a BRV by successive probabalistic observations 
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#1
Jul210, 02:35 PM

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[I have been struggling with this problem for weeks]
Suppose you are wondering about the outcome of a coin flip. You cannot observe the coin directly, but you have 3 tests you can perform to increase your confidence. Before you perform any tests, all you know is p(heads) = 0.5. Say the first test is to feel the surface of the coin. If it feels smooth, then there is a greater chance the coin is heads, suppose p(headssmooth) = 0.7. Say the second test is to run your finger nails across the surface. If you hear no scratching noise, then there is a greater chance the coin is heads, suppose p(headsno scratchy noise) = 0.8. Say the third test is to peak into the cup of your hands. If you see a slight glimmer in the darkness, then there is a greater chance the coin is heads, suppose p(headsslight glimmer) = 0.6. Also assume that each of these tests are independent. What other assumptions can you make that allow you to estimated p(heads  (smooth) & (no scratchy noise) & (slight glimmer))? 


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