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fluidistic

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**Note: not homework; thread moved to biology**

1. Homework Statement

1. Homework Statement

It is not a textbook problem, but a real life scenario, as such I am not sure the solution exists.

A child is born with a rare genetic condition (1 chance in a million). There is about 1/3 chance it comes from a mutation that occurred only in him and 2/3 chance that it comes from his mother (carrier). I want to calculate the probability that the sister of the mother of this child is a carrier of that genetic disorder. But I have more information that do impact on such a probability: the grand mother of that child has had 3 children. One is a boy (no genetic disorder), 2 are girls. Both of these girls got 1 (son) child, 1 ill, the other safe.

The genetic disorder is recessive and on the X chromosome, hence only boys do display signs of the condition, while women are carriers (theoretically they could be affected but this has never occurred as far as we know) but show no sign.

Also note that a carrier has 25% chances to give birth to an ill son, 25% to a non ill son, 25% to a non carrier daughter and 25% to a carrier daughter.

## Homework Equations

Bayes theorem?

## The Attempt at a Solution

Only thoughts for now. I was wondering whether I could apply Bayes theorem several times in a row to solve the problem, or whether it is more complex than that, or whether we have not enough information to solve it.

If I start with a first estimation, the mother of that child has 66% of being a carrier, so the grand mother has, at first order of estimation, (2/3)^2=4/9=44.4% chances of being a carrier. However the fact that the grand mother got a son without this genetic disorder should lower that probability, and similarly for the fact that the other daughter has had a non ill son.

In the end it looks like I'm seeking to calculate the probability that the mother "A" is a carrier, given that her sister "B" has 2/3 chances to be a carrier.

Lastly, if I ever get that result, I wish to combine it with another totally independent "test" that claims that the mother "A" has 5% chances to be a carrier. How would that number lower given the prior calculations.

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