# Independence (5 of 5)

An interesting failure to appreciate the independence of events is called the "gambler's fallacy." A simple illustration of the gambler's fallacy is the commonly-held belief that a fair coin that has come up heads five times in a row is more likely than not to come up tails on the next flip. One reason for this misconception may be the notion that the number of heads and tails balances out in the long run. If there are more heads now, the balancing process will produce more tails in the future. The flaw in this reasoning is that the number of heads and tails do not balance out in the long run. If you flipped a coin 1,000 times, the probability of obtaining exactly 500 heads is practically zero. What happens in the long run is that the proportion of heads approaches 0.5.

There are other contexts in which people are likely to see events as being dependent when they are not. One study of basketball players by Tversky and Kahneman revealed that although conventional wisdom holds that players "get hot" and have streaks of baskets, a careful analysis showed no evidence of hot streaks. Instead, the probability of making a basket was independent of the success on previous shots.