Many, many people have made incorrect assumptions based on probability. Some of the most obvious cases come from people who gamble. For instance, gamblers often believe that if certain events (numbers on a pair of dice or a roulette wheel, or results on a slot machine) have not occurred in some time, then these numbers or results are "due" to occur. Or, they assume that if a repeated behavior results in several losses in a row, then they are "due" for a win if they repeat the same behavior. (Note that most casino games are designed so that the odds are slightly in favor of the casino. The games are otherwise "fair," in terms of their setups and theoretical probabilities for possible outcomes.) Apply the concept of expected values, as well as your understanding of "fair" games, to explain why gamblers are wrong when they use this line of reasoning After you post your thoughts, read and respond to the posts of your peers by using probability and mathematical reasoning to add insight to their conclusions.
