Is there a good survey article for lay readers (imagine an intelligent secondary-school pupil who may later do graduate work in philosophy but doesn't yet know much) of the philosophical difficulties attending the problem of induction, and the positions that philosophers have taken on it?
I would suggest Charles Sanders Peirce's essay, Some Consequences of Four Incapacities, which can be found in a number of different books and collections. His Lowell Lectures are perhaps more comprehensive (though painstakingly so). It is an extremely interesting piece by one of the world's greatest logicians. My only hesitation to suggest it is that it is not easy. But look at the first few paragraphs here, and see if you think it works. I have a feeling that this is the sort of thing you were looking for––though maybe a bit more abstruse than you wanted.