To me, that scenario just about sums up being gullible. Gullible people will fall for anything, every time. Naive people like to hope for the best, like to believe people, so they will be swayed by a salesman, but they'll still have a bit of independent thought. Innocent is simply what it says - innocence may lead them to believe what someone says, or it may not. Depends how gullible they are!

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Note added at 39 mins (2012-09-06 21:47:03 GMT)
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Of course, it depends on how young this person is - we all go through a naive period, but some very young kids have already gone through that to become quite streetwise. Should a "little girl" be making this decision off her own bat?

Of course, if this is the same one who made a medicine cake (see another KudoZ question), then she's clearly very stupid and perhaps we should be looking for different adjectives.