How Do You Calculate the Probability of a Child Being Affected by Genetics?

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Discussion Overview

The discussion revolves around calculating the probability of a child being affected by a genetic condition, specifically focusing on the implications of parental genotypes and carrier status. The scope includes theoretical reasoning and mathematical calculations related to genetics.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant calculates the probability of a child being affected as 1/4, assuming both parents are carriers of the affected allele.
  • Another participant questions the initial assumption, asking about the probability of the parents being carriers given that they have siblings with the disorder.
  • A third participant provides a detailed calculation based on the pedigree, suggesting that the probability of the child being affected involves multiple factors, including the likelihood of each parent being heterozygous.
  • This participant calculates the probability of both parents being heterozygotes as 4/9 but expresses confusion over a key that states it is 2/3.
  • A later reply suggests that the probability for each parent being heterozygous is indeed 2/3, but notes that this is not clearly expressed in the problem.

Areas of Agreement / Disagreement

Participants express differing views on the calculations and assumptions regarding the probabilities of parental genotypes and carrier status. There is no consensus on the correct interpretation of the probabilities involved.

Contextual Notes

Participants highlight potential limitations in the clarity of the problem statement, particularly regarding the probabilities of the parents being heterozygotes and the implications of having affected siblings.

Who May Find This Useful

This discussion may be useful for individuals interested in genetics, probability calculations in genetic inheritance, and those studying or working in fields related to genetic counseling or medical genetics.

TytoAlba95
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Homework Statement
What is the probability that the child will be affected and the parents will be carrier?
Relevant Equations
N.A.
IMG_20190816_123013095.jpg


My Attempt: For the child to be affected, both the parents must be carriers.
Hence P(child)= Probability of the father of passing down an affected allele x Probability of the mother of passing down an affected allele
= 1/2 x 1/2
=1/4
The answer is (a).
I'm completely lost. Please help.
 
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The probability is 1/4 if both parents carry the affected allele. But what is the probability of that? You know they don't have the disorder, but each has a sibling who does. What does that tell you about the probability of their being carriers?
 
IMG_20190816_123013095.jpg


Since the pedigree shows an autosomal recessive trait, the genotypes of the 1st generation parents are:

Untitled.png


Thus, P(child being affected) = Probability of father being heterozygote x Probability of the father passing down the mutant allele x Probability of mother being heterozygote x Probability of the mother passing down the mutant allele
= 2/3 x 1/2 x 2/3 x 1/2

Reasons (chronologically):
a) 2/3 - From a cross between I-1 and I-2 heterozygote parents, there are only three possibilities of getting a phenotypically normal individual out of which 2 can be heterozygote.
b) 1/2 - The II-2 must be a heterozygote for III-1 to be affected, and out of his two allele, only one can be mutant, that can be passed on.
c) same as a
d) same as b

Now coming to the second question, here I have a problem accepting the key.
P(both the parents being heterozygotes)= 2/3 x 2/3 =4/9.

But the answer is 2/3 only?!
 
It must mean the probability for each parent is 2/3. It is not very clearly expressed.
 
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