Problem of finding which population a sample came from

The following problem has it's basis in Quantum Mechanics:

Part 1) There are two tribes the Eddas, a friendly tribe, and the Thors, a hostile tribe (ignore the Aeolians and the Boreans for this part of the problem)

An anthropologist has to study one or the other of these two tribes after being dropped into the area where the tribes live. He knows the differentation in eye color between the tribes but nothing else; if he accidentally chooses to study the Thors he will be killed. If the Eddas are chosen he will win a nobel prize.

1. How does he decide which tribe is which after landing?

2. What is the probability he can tell whether he is with the Thors, the Eddas?

The solution is given below. I have added definitions for part 2. They are the same as already mentioned in part 1.

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1. How does he decide which tribe is which after landing?

The way to differentiate between the 2 tribes is by sampling people from the tribe and determining their eye color.
Since, we know the probability of grey and blue eyes in each tribe, the number of grey(or blue) eyed people will be binomially distributed.

For example, if he picks 100 people and records their eye color, then the number of grey eyed people follows a binomial
distribution.

The chance of exactly k grey eyed people for Eddas is ...

Solution Summary

How to determine if a sample came from the friendly Eddas tribe or the hostile Thors tribe based on eye color proportions?

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