FOM: A problem in Foundations of Statistics

[JoeShipman@aol.com]

The foundations of statistics are in such a state of non-consensus that even the following completely basic problem does not have a generally agreed-upon solution.

Given: an event has occured a times and failed to occur b times in m=a+b trials.  What is the chance that it will occur c times and fail to occur d times in a further n=c+d trials?

I could discuss here several solutions that have been proposed in the statistics literature, but I would like to see what FOMers have to say first, not wishing to influence any fresh approaches with previous work.

-- Joe Shipman