Here is an easy math puzzle. Suppose we have 3 random variables a,b and c with c=a+b. We round a to A, b to B and c to C and want to know the chances that C=A+B. We need some more information for an unique answer. So for definiteness let a and b be random real variables uniformly distributed between 0 and 50. Let c=a+b and let A,B and C be a,b and c rounded to the nearest integer (it won't matter how .5 cases are rounded). Then we ask what is the probability that C=A+B?
This problem was inspired by the recent furor regarding the Research 2000 polling operation in which it has been suggested that Research 2000 was saving money by making up its poll results. However it is unclear if the above problem actually has any connection to the anomalies that have been found in the Research 2000 results.
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