Rounding Errors

 The Problem, disguised a little ...

 The government have decided there is not enough money for them to continue to support both motherhood and apple pie: only one of the two can be funded. So the Ministry for Awkward Decisions asks the Department of Useless Numbers Calculations and Experiments to tell them whether the electorate think apple pie is more important than motherhood. The officials at DUNCE, having asked two people in the corridor and one in the lift what they think, write down a random number between 0 and 1 that they claim is the proportion of the population in favour of motherhood. To add verisimilitude to an otherwise bald and unconvincing number, they include a vast number of digits after the decimal point, before passing the number back to MAD. Here, the first official to see the number decides that the people at DUNCE have gone over the top with the number of digits, so he cautiously rounds the number to one fewer digits. The next official does likewise, and the next, until when the number reaches the Minister, it has lost all its decimal digits: it is a whole number, either 0 or 1. The Minister, not unreasonably, concludes that the people in the survey were unanimously in favour of what?

 

What is the probability that apple pie will win?

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Last modified: June 18, 2007