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Intel Customer Support Technician
According to the available documentation, you need a processor with at least Intel HD Graphics 4000 in order to play Minecraft. So, to answer your question, no, there is no driver update that is going to help you. I believe the requirement is for OpenGL; the minimum version required didn't exist at the time the Intel HD Graphics 3000 was last updated (and no, since it is embedded in the driver, it is not possible to upgrade just this component).
Sorry, time for a system upgrade,