"Many psychological experiments were conducted in the late 1950s and early 1960s in which subjects were asked to predict the outcome of an event that had a random component but yet had base-rate predictability - for example, subjects were asked to predict whether the next card the experiment turned over would be red or blue in a context in which 70% of the cards were blue, but in which the sequence of red and blue cards was totally random.
In such a situation, the strategy that will yield the highest proportion of success is to predict the more common event. For example, if 70% of the cards are blue, then predicting blue on every trial yields a 70% success rate.
What subjects tended to do instead, however, was match probabilities - that is, predict the more probable event with the relative frequency with which it occurred. For example, subjects tended to predict 70% of the time that the blue card would occur and 30% of the time that the red card would occur. Such a strategy yields a 58% success rate, because the subjects are correct 70% of the time when the blue card occurs (which happens with probability .70) and 30% of the time when the red card occurs (which happens with probability .30); .70 * .70 + .30 * .30 = .58".
Can this make people believe that they are over-confident?