From Longman Dictionary of Contemporary Englishbe drawn/pulled/picked out of the/a hatbe drawn/pulled/picked out of the/a hatif someone’s name is drawn out of a hat, they are chosen, for example as the winner of a competition, because their name is the first one that is taken out of a container containing the names of all the people involved The first correct entry out of the hat on September 2nd will win a prize. → hat
