Safest - Never update by clicking on a popup window.
When you get a popup such as the Flash out of date for example - close the popup window and go directly to the website in question by typing it's address in the address bar - in this case adobe.com (or the specific page on their site for Flash is http://get.adobe.com/flashplayer/
And the same goes for updating Java.
Always update Java and Flash directly from the vendor's website, NEVER through a pop-up of some sort !
It can not be stressed enough
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