A low number statistics probability-problem (genetics)

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Discussion Overview

The discussion revolves around a probability problem related to genetics, specifically concerning the inheritance patterns of a disease affecting a subset of siblings. Participants explore the implications of having 3 out of 5 siblings affected by the disease and the likelihood of the disease being dominant versus recessive.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that the higher than expected rate of affected siblings indicates the disease may be more likely to be dominant rather than recessive.
  • Another participant argues that without knowing the genetic status of the parents, the problem cannot be accurately assessed, as the expected 1/4 rate applies only under specific conditions.
  • A later reply clarifies that only one parent is affected, which changes the expectations for inheritance patterns.
  • Some participants propose that the genetic composition of both parents can be determined based on the symptoms observed in the siblings, which could help solve the problem.
  • One participant mentions that their calculations suggest a 1 in 2 chance of a child being affected, regardless of whether the inheritance is dominant or recessive, questioning the assumption that the observed rates favor dominance.
  • Another participant acknowledges that the presence of both affected and unaffected siblings provides some information, but emphasizes the need for population rate estimates to draw further conclusions.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the observed sibling outcomes for determining the inheritance pattern. There is no consensus on whether the disease is more likely to be dominant or recessive, and the discussion remains unresolved regarding the probability calculations.

Contextual Notes

Limitations include the lack of information about the parents' genetic status and the assumptions made regarding the population prevalence of the trait, which affect the validity of the probability estimates discussed.

B0b-A
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A probability problem (genetics), not homework, honest.

3 of 5 siblings are affected by an unknown inherited disease*.

That this outcome is higher than 1 in 4 which is typically the case in recessive traits suggests that the disease is more likely to be dominant than recessive.

Given 3 of 5 siblings are affected how much more likely is it that this genetic illness is dominant rather than recessive ?.

Like I said this isn't homework so I can't confirm if any answer given is correct.

[ *adult onset : inheriting the trait would not make their birth less likely ].
 
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Without knowing the status of the parents, I don't think this problem works. In particular, the 1/4 is expected only in a case where a dominant trait would not appear at all.

With assumptions about their health, you can calculate the likelihood for both hypotheses and compare them.
 
mfb said:
Without knowing the status of the parents, I don't think this problem works.

In this case only one of the parents of the five siblings is affected (symptomatic).
(sorry forgot to mention that :redface: ).
 
Then there is no reason to expect a rate of 1/4.

Based on the information that neither zero nor all childen got symptoms, you can determine the genetic composition of both parents in both cases and solve the problem.
 
mfb said:
Then there is no reason to expect a rate of 1/4 ...

OK now I see 1in 4 is only expected in recessive inheritance where both parents were unaffected carriers: both carry one copy of the disease gene. But in this case one parent was affected.

mfb said:
... Based on the information that neither zero nor all childen got symptoms, you can determine the genetic composition of both parents ...

If it were dominant the affected parent cannot have two copies of the disease gene, otherwise all the children would be affected.

If recessive the unaffected parent must have a copy of the disease gene, otherwise no children would be affected.

mfb said:
... you can determine the genetic composition of both parents in both cases and solve the problem.

Now my possible punnet squares are giving me 1 in 2 odds that a child would be affected, whether it was dominant or recessive inheritance.

So that it affected 3 of 5 siblings doesn't make it more likely to be dominant than recessive (?)
 
Last edited:
Correct.

You could argue that the information "some do not get the trait, some do" itself is some information, but then you need some estimate about the total rate of the trait in the population.
 
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