Well, there is a certain arithmetics proof which I am sure many have
heard before. I was prodded to transform this into a probabilistic
argument.

The probability of meeting a horse with 15 legs is zero and if you meet
a horse then the probability that the horse has 4 legs is one.

Since the events of a horse having "4 legs" and "15 legs" are mutually 
exclusive (disjoint events) and so independent we can add up these 
events and their probabilities which results in the following: Should we 
meet ever a horse at some time [this is a real restriction to people who 
live in cities] then the horse will have (4+15=)19 legs with probability 
(1+0=)one.

P.S. The usual version runs: 

Every horse has 4 legs more than no horse, no horse has 2 legs, therefore
horses have six legs. (Arithmetic version) 

Comparing the numbers of lines this probability joke takes up with the short 
proof in arithmetics it is no wonder that that probability theory is so much 
harder to understand than arithmetics. 

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