There are several forms of probability fallacy, with several names to identify the concept. Basically any fallacious reasoning that is related to probability can be called a probability fallacy. Some of the more well known names and types are: gambler’s fallacy, conditional probability fallacy, prosecutor’s fallacy, the zero probability fallacy and others, depending on how much attention is being paid to the specific conditions that lead to fallacy in using probability to support an argument or hypothesis.
The probability argument has the following: There is information that gives support that an event or condition is probable. There are rules for figuring out probability. If the rules are followed, then there is good probability.
If the rules are violated or are not followed, then fallacy results. A basic understanding of the rules is helpful in understanding how they can be broken.
There is a base rate fallacy, where the base rate is the frequency or rarity of an event, overall. This is also called generic information. A specific case is not examined. When the base rate or generic information is ignored and only the specific case is used to support probability, then a fallacy occurs. It is based on a tendency to use specific information and to ignore generic information, even when both types of information are available. Generally, it is best to use all of the information that is available in order to prevent missing some mistake, detail or fact that might be important when trying to predict probability.
In the conjunction fallacy, two or more things are claimed. There can be no more truths than the truths that are claimed. For example:
Statement 1. The restaurant will open and will sell food.
Statement 2. The restaurant will open, will sell food, and will make a profit in the first day.
Which is more likely to be true?
This is a conjunction and the conjuncts are opening and selling food. There will be no selling of food if the restaurant is not open. If food is sold, then the restaurant had to have opened. For the second statement to be possible, both conjuncts must be true: the restaurant must be opened and food must be sold in order for there to be a probability of profit. Therefore the first statement is more likely than the second statement.
The Gamblers Fallacy and the Hot Hand fallacy are based on ignoring the fact that each event has probability that is independent of any other event. When a game is truly based on randomly generated, statistically independent factors, (or is not “fixed”), there are the same odds for each spin of the wheel or roll of the dice or hand of cards. A string of bad or good events is no indicator that the next event will be influenced by the previous events.
In the multiple comparisons fallacy, deductive reasoning comes into play. In deductive reasoning, there is a chance that, while the evidence is true, the conclusion might be false. This requires a decision about confidence that the evidence supports the conclusion, which is rarely 100 percent confidence. If a study group is exposed to a substance and a significant number of them contract a disease that is related to the substance and no other known factor, is it 100 percent likely that the control group that is not exposed to the substance will not contract the same disease? This has created problems for concluding that exposure to electromagnetic fields causes cancer, while cigarettes and cancer are far more likely to be seen as probable.
In summary, the basic descriptions of the common probablity fallacies is covered. The links below will provide more understanding of the concepts that are involved.
Fallacy Files, “Base Rate Fallacy”
Fallacy Files, “Conjunct Fallacy”
Fallacy Files, “Gambler’s Fallacy”
Fallacy Files, “Multiple Comparisons Fallacy”
Norman Fenton, “Probability Theory and Bayesian Belief Bayesian Networks”