P(A) = 0
A recent event (see next paragraph) provides a good example of an event where Probability P(A)=0, yet the event A could occur (i.e. A is not impossible). Students should be able to follow the logic of this example better than facing the old stand-by claim for a coin flip: P(H)=P(T)=0.5 and P(edge)=0...and yet it is possible that a coin could land on its edge!
Scott Travers, a writer about coins or other numismatic matters, is deliberately paying for items using three rare pennies--a 1914 penny worth $350, a 1908 penny worth $200, and the 1909-S-VDB penny worth $1000. In each case, he is pretending they are normal pennies worth one cent.
Scott's intent is to "salt" the public coffers, with the hope that people will look carefully at their change and discover "the magic of coin collecting." One last important fact--he is putting the coins into circulation in New York City.
Thus, as an example of interestring mathematics, I claim that zero is the probability P of my finding one of these three pennies in the great Northwest, yet it is possible. Sorry, no more time to write...I have to check my pocket change....
Source: Bellingham Herald, April 15, 2006