Two Dice Challenge

You have two dice in a shaker. You ask a friend to shake the dice and peek at the outcome, which he does. You ask him, "Is at least one of the dice a two?" He says, "Yes." What is the probability both dice are a two?

In this video, a challenger accepts my offer to pay 8 to 1 odds for two 2's, as long as there is at least one two. Watch to see who wins, after over 300 shakes of the dice.