[read this on g+]
With the release of Google+, I've been thinking about privacy and social.
You buy a particular brand of jelly from your local grocer from time to time. On the inside of the jelly jar lid is printed a number, which you come to know from your grocer is the number of that jar within the batch, which is always between 1 and the batch size.
Two aliens are chatting.
Humans are weird, a grating robotic noise, spewing green smoke and dribbling a caustic glue-like substance.
You have a 100-sided fair die and you are testing for the event that a 37 is rolled. You don't have direct access to observe the die, however, you must rely on a complicated technology that observes the face of the die and reports the result to you; when you run a trial, the system lights either a green LED ("rolled a 37") or a red LED ("did not roll a 37"). The equipment that observes the rolled number, however, is not perfect—on average, 1 out of every 50 trials the system fails to read the number properly and observes a random value equally distributed between 1 and 100.
(The very astute observer will further note that there is another incorrect contingent probability in the table above, but I leave it to you to figure out.)
So, how can I achieve the correct behavior I was after? I should have said that the switch controlling which LED to light is flaky, and lights the wrong LED 2% of the time. So let's pretend that's what I said all along, and we can put this whole thing behind us. :-)