What is the probability of a mated triple with three sexes in sea-creatures?

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SUMMARY

The discussion centers on calculating the probability of forming a "mated triple" from a newly discovered sea-creature species with three indistinguishable sexes. The problem involves conditional probabilities and counting methods, specifically utilizing Bayes' Theorem and the Law of Total Probabilities. Participants suggest that the assumption of equal likelihood among the sexes is crucial for solving the problem. The initial approach involves determining the probability that all captured specimens belong to only two of the three sexes.

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Homework Statement



A new lifeform has been discovered in the sea. In particular, these sea-creatures
come in THREE sexes, which are indistinguishable (except by other sea-creatures). If A robot captures N specimens, what is the probability these
chocies will allow a “mated triple” with its promise of more little sea-creatures to come?


Homework Equations


This homework is supposed to be on conditional probabilities and counting methods, so I suppose Baye's Theorem and Law of Total Probabilities would be useful


The Attempt at a Solution


Unfortunately, I truly have no idea where to begin this problem.
Any ideas?
 
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I suspect you are to assume the genders are equally likely in the sea-creature population.

I would first try this indirectly but trying to calculate the probability that all N creatures belong to two identical genders.

--Elucidus
 

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