No matter how we feel about card magic, everyone is familiar with the inevitable invitation to: “Please pick a card, any card.” And then the magician uses one of thousands of existing methods to prove that they already knew which card it would be.
If we look at the effect through the eyes of a spectator who happens to be a statistician, they would probably calculate: “The chance that I will randomly draw the predicted card from 52 cards is 1 in 52. That’s just under 2 in 100 cases—very unlikely. So the magician must have cheated.” This is true, of course.
There is a convention in statistics—by agreement, results with a probability of less than 5 out of 100 (i.e., 5%) are considered “significant,” meaning they are noticeable and probably not a coincidence. An example from medicine: A company is testing a new drug. The study shows a positive effect, but the probability that the effect could be a coincidence is 6 out of 100. Since this is above the 5% threshold, the drug is not developed further. However, if the number were 2 out of 100, as in our card trick, the result would be considered “highly significant,” and the company would invest.