What Is Random Behavior

A basketball player who makes 70% of her free throws has missed four in a row. Before her next shot, someone in the stands is sure to say that she is “due” to make this one. You have lost card games to your friends every night this week; you think to yourself, “Well, next week I’m due to win a few.” A couple has three children, all boys. “The next one is due to be a girl,” a friend remarks. Each of these events, the free throw, the card game, the birth of a child, involves chance outcomes that cannot be controlled. In the long run, the basketball player makes 70% of her free throws, you may win 60% of the card games, and approximately 50% of the babies born are girls. But do these long-run facts help us to predict behavior of random events over the short run?