While you may not pay for free apps, many aren't actually free. You pay for them by viewing ads that pop up at the bottom of the screen or by agreeing to share some of your personal data. You should know how you're paying, though. However, security researchers at SophosLabs have found more than 50 apps available through the Google Play store that secretly steal personal data.
Many of these apps claim they don't share any personal information because the app isn't designed to share your information. However, these apps use Android XavirAd to serve up ads onscreen, and that adware does collect your information and send it to a remote server.
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