Combining n simultaneously occuring probabilities of an event occuring into one summative probability

I am a bit lost with regards to the problem described a bit further down, because though many methods to approach it are documented in available literature, the verdict as to which model is the most reliable is not by any means unanimous. Without any further ado, what is the most reliable statistical model to do the following:

n present factors are weighed against n absent factors, to come to a percentual indication/chance of an event taking place (between 0-100%). The outcome variable is thus continuous. The data to work with is an incidence percentage of a specific factor in an event.

An example would be:

In a population of marbles, there are those with a golden core and those without one. Of the marbles with a golden core, 70% have red spots on them, 65% green spots, and 60% blue spots.

Logistically speaking, if a marble has multiple, coloured spots, the probability of that marble having a golden core should increase, at least logistically. Returning to the example, two random marbles are taken, Marble 1 and 2 respectively.

• Marble 1 has red spots AND green spots, but NOT blue spots.
• Marble 2 has red spots AND green spots AND blue spots.

Because the factors/variables are not independent, simply multiplying the probabilities does not seem to yield the correct answer. Alternatively, Bayes theorem, which could have been applied, is not applicable because the spotting of the marbles WITHOUT a golden core is not known. The only thing that is known is the spotting in the group of marbles WITH a golden core. Conflation theory, with retrospective normalisation, could be applicable, however, I do not know if it is the most reliable fashion of combining the factors in order to assess the probability of a marble having a golden core. Similarly, Venn diagrammatic summation of probabilities may be applicable, though again, possibly not so reliably.

Thus, in all, how can one combine the probabilities of the present factors/variables and absent factors/variables, in order to come to a summative probability of an event occurring, in this case, how can one combine the colour of present spots (R/G/B) and absent spots (R/G/B) to approach whether a marble has a golden core.

• Doesn't seem possible without making some assumptions about the marbles without golden cores (I wonder what the "many methods to approach it" "documented in available literature" are). – Juho Kokkala Sep 3 '16 at 20:19