What does this law say about the probability of an event? Perhaps you have also heard of something called the Law of Averages (also called the Gambler's Fallacy).

Are these the same laws? If not, how are they related and how are they different?

What general misconceptions do people have regarding these ideas?

Consider the following scenarios, commenting on the validity of the reasoning that is being used. After an unusually dry autumn, a radio announcer is heard to say, "Watch out! We'll pay for these sunny days later on this winter." A batter who had failed to get a hit in seven consecutive times at bat then hits a game-winning home run. When talking to reporters afterward, he says he was very confident that last time at bat because he knew he was "due for a hit."

Commercial airplanes have an excellent safety record. However, in the weeks following a crash, airlines often report a drop in the number if passengers, probably because people are afraid to risk flying. A travel agent suggests that, since the law of averages makes it highly unlikely to have two plane crashes within a few weeks of each other, flying soon after a crash is the safest time. In a Monte Carlo casino in 1913, the color black came up a record twenty-six times in succession in roulette. There was a near-panicky rush to bet on red, beginning about the time that black came up the fifteenth time. Why?