It works:
$('.child').hide();
$('.parent').hover(
function() { $(this).children('div').show() },
function() { $(this).children('div').hide() }
);
An example is http://jsfiddle.net/4kMuD/ , although identifiers are used for the selector, not classes.
I assumed (although you did not say) that you want the child div to disappear again when you no longer hang over the parent.
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