Question

Why is the gambler's fallacy incorrect in its assumption that the 6th coin toss will be tails if the 5 previous have been heads?

a) deductive reasoning
b) representativeness heuristic
c) law of large numbers
d) distinctiveness principle

Answer 1

The gambler's fallacy is incorrect because each coin toss is an independent event and is not influenced by previous outcomes. The law of large numbers explains that as the number of repetitions of an experiment increases, the observed frequency of an outcome tends to approach the theoretical probability. Therefore, the 6th coin toss will not necessarily be tails if the previous 5 have been heads.

Step-by-step explanation:

The incorrect assumption made in the gambler's fallacy is due to a misunderstanding of probability. Each coin toss is an independent event, meaning the outcome of one toss does not affect the outcome of the next. The correct reason why the 6th coin toss will not necessarily be tails, even if the previous 5 have been heads, is due to the law of large numbers. This law states that as the number of repetitions of an experiment increases, the observed frequency of an outcome tends to approach the theoretical probability. In the case of a fair coin, the theoretical probability of getting heads or tails on each toss is 0.5, regardless of the previous outcomes.