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The appeal to probability is a logical fallacy, often used in conjunction with other fallacies. It assumes that because something could happen, it is inevitable that it will happen. This is flawed logic, regardless of the likelihood of the event in question. The fallacy is often used to exploit paranoia.

This has the argument form:

Possibly P.

Therefore, P.

Equivalently, using modal logic and logical connective notation:

→

Some examples are:

• "There are many hackers that use the internet. Therefore, if you use the internet without a firewall, it is inevitable that you will be hacked sooner or later."
• "AMD has been catching up to Intel in recent years. In a few years they will definitely take over Intel's position, and eventually put them out of business altogether."
• "When soccer becomes popular in a town, hooliganism will become a major problem. Thus, if we allow a soccer team in our town, we will be overrun by hooligans." (also a False cause fallacy)

While not considered a "true" fallacy by some (because it is rarely used by itself), the appeal to probability is a common trend in many arguments, enough for many to consider it a fallacy of itself.

The logical idea behind this fallacy is that, since the probability is very high, it is best to act as if it is true, which is especially true in the case of Example #1. This fallacy is also related to the 'umbrella joke' - If someone ever forgets his or her umbrella, that will be the one day that it actually rains.

Another, somewhat more complicated example of this fallacy is the idea of 'The Singularity'. This is a hypothesis propounded by some scientists and futurists which asserts that, based on historical trends, it is reasonable to assume that in the relatively near future, a time will come when progress in science and technology will be so rapid that humans will no longer be capable of understanding it. Many doubt such an event could happen, but proponents argue that it is a historical inevitability. The probability of it would be so high that it would be historically absurd to imagine that it will not happen in some way, not because it is an event with a fixed high probability of happening at any given time, but because it is an event the probability of which is small in the past, but which increases exponentially over time. Basic calculus would seem to imply that an event with a probability that increases exponentially actually is inevitable, because as we follow time forward, the probability of it not happening becomes infinitesimal.