Final answer:
No, observing five heads in a row does not guarantee five tails in a row; each flip is independent with a 50% chance. This misunderstanding is called the Gambler's Fallacy, and the Law of Large Numbers explains that only over many trials will the relative frequency of heads and tails converge on the theoretical 50% probability.
Step-by-step explanation:
Observing five heads in a row when flipping a coin does not guarantee that you will observe five tails in a row to balance the probability to 50%. This is because each coin flip is an independent event, and the probability of getting heads or tails on any single flip is always 50%, regardless of previous outcomes. This misconception is a common example of the Gambler's Fallacy, which is the incorrect belief that past events can influence the likelihood of future independent events to 'balance out' probabilities.
The principle that explains why you should not expect exactly five heads and five tails in a set number of flips is the Law of Large Numbers. According to this law, the relative frequency of an outcome (such as heads or tails) will approach the theoretical probability (in this case, 0.5) as the number of trials increases. However, this convergence towards the theoretical probability occurs over a large number of flips, and short-term sequences can deviate significantly from expected ratios.
Moreover, each microstate (specific sequence of outcomes) is equally probable, meaning that getting five heads in a row is just as likely as any other specific sequence of five flips. Therefore, having already seen five heads does not make five tails any more likely in the following flips.