TITLE: What is the easiest randomized algorithm to motivate to the layperson?
QUESTION [33 upvotes]: When trying to explain complexity theory to laypeople, I often mention randomized algorithms but seemingly lack good examples to motivate their usage.  I often want to mention primality testing but the standard randomized algorithms don't admit a simple description (or proof of correctness) in a lay-atmosphere.  I often resort to the saying that randomized algorithms allow "finding hay in a haystack", but that has little mathematical substance.  
The question: Is there a good example of a problem that:

is easily explained (and sufficiently interesting)
has a simple randomized algorithm
appears non-trivial to get an efficient deterministic algorithm

and ideally also satisfies:

the randomized algorithm has a somewhat understandable proof of correctness - so no Markov/Chernoff/random-walk-mixing-times

REPLY [3 votes]: Multiplication checking: is $ab$ equal to $c$ (or is $a(x)b(x)$ equal to $c(x)$)? Analysis of randomized solution is pretty easy; also it provides a huge gap in asymptotic compared to straightforward multiplication.