Assume we want to know the probability that two events co-occur (i.e. of their conjunction). If the two events are independent, the probability of the co-occurrence is the product of the probabilities of the individual events, P(A and B) = P(A) * P(B).

In order to estimate the probability of some event, one method would be to decompose that event into independent sub-events and use this method to estimate the probability. For example, if the target event E = A and B and C, then we can estimate P(E) as P(A and B and C) = P(A) * P(B) * P(C).

Suppose we want to make an event seem unlikely. If we use the above method but slightly under-estimated the sub-event probabilities and use a large number of sub-events, then the resulting final probability will inevitably be very small. Because people tend to find moderate-range probabilities reasonable, this would be a superficially compelling argument even if it results in a massive under-estimation of the final probability. This has been called the multiple-stage fallacy.

Assume we want to know the probability that either of two events occurs (i.e. of their disjunction). If the two events are [...]

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https://www.thefloatingdroid.com/disjunctive-arguments-can-be-a-reverse-multiple-stage-fallacy/

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