This question is inspired by one asked at MathOverflow. (These questions at Cognitive Sciences and at Cross Validated might also be relevant.)
Are there any studies on what choices humans commonly make when asked to think of a choice "at random"?
For example, this website claims that when people are asked to think of a card (in a standard 52-card deck), they often select the nine of diamonds, the ace of spades, the queen of hearts, or the six of clubs. Or when a person is asked to think of a number between 1 and 1,000, they will often select 333.