What if I told you to choose a card at random? Simply choose one from a standard deck of 52 cards, think of a card, do not draw one from a real deck... Make sure you have one in mind before you read on.
Assuming that you have a card in mind, I bet you chose the Ace of Spades. Of course, I don't know the card you were thinking of, but that is the one I bet on. Every textbook on probability says that I have a 1/52 chance of having guessed right. Actually, that is not quite true... About one out of 4 readers will choose the Ace of Spades, and one out of seven will choose the Queen of Hearts, as shown by a study of the researcher in psychology of magic Jay Olson and his collaborators.
In this experiment, is the choice of a card purely random? And what does random mean anyway? Even if purely random is not properly defined, most would agree that it means no information at all, or completely unpredictable. The outcome of the experiment above is clearly not what you would call purely random. But...