A nice question turned up on Math SE last week:
This is either very easy, or a pain in the butt, depending on whether you go about it the right way. (OP tried the hard way, and got an utterly wrong answer.)
I think it's a nice question because it is highly instructive for people who don't know much about probability: you can get the answer to this one without knowing much about probability. I asked Katara, who does not know very much about probability, to see if she would try the easy way.
She didn't. She decided to do it the hard way, and then correctly recognized that she didn't know enough technique to actually do the calculation. (I told her that I wouldn't have asked if that had been the only way to do it, but that didn't help.) She seemed pleased when I showed her the easy way. Here's how I explained it:
I think this is a very neat way to put it. Of course it's quite possible that this explanation might not work — nothing works for everyone — but this time it did.
I also told her that her idea would have worked, and that if done correctly it would have produced the same answer at the end. At some point maybe she'll learn to do probabilistic calculations and I'll show her. (“Hey, remember that problem about the bird eating the fruits?”)