There are other ways of combining individual probabilities for different words than using the "naive" approach.

These different hypotheses result in radically different formulas for combining the individual probabilities.

For example, assuming the individual probabilities follow a chi-squared distribution with 2N degrees of freedom, one could use the formula:

Now, let's calculate the individual probability of a 2-2 split when missing four cards (the following row in the table).

For this kind of judgment, anchoring on the individual probabilities results in an overestimate of the combined probability.

It is these individual probabilities that make the aggregate certainty.

In the second stage, the researcher corrects for self-selection by incorporating a transformation of these predicted individual probabilities as an additional explanatory variable.

Formalising this insight required transformations to be applied to the cumulative probability distribution function, rather than to individual probabilities (Quiggin, 1982, 1993).

If the distribution is discrete, the individual probabilities of all possible values of are computed, and then summed to find the normalization constant.

P(A) is equal to the product of these individual probabilities: