Genetic Probability (Binomial Expansion)

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SUMMARY

The discussion focuses on calculating the genetic probability of having 2 boys and 2 girls, with one boy being albino, given that one parent is albino and the other is a heterozygous carrier. The binomial expansion coefficients for this scenario are established as 1, 4, 6, 4, 1, leading to the equation (p^4) + 4(p^3)(q) + 6(p^2)(q^2) + 4(q)(p^3) + (q^4). The key challenge is integrating the 50% probability of albinism into the overall calculation, which can be approached by considering the probabilities of the children’s genders and the specific genetic traits simultaneously.

PREREQUISITES
  • Understanding of binomial expansion and its coefficients
  • Knowledge of basic genetics, specifically inheritance patterns
  • Familiarity with probability calculations in genetics
  • Ability to manipulate algebraic expressions involving probabilities
NEXT STEPS
  • Study the application of binomial expansion in genetic probability scenarios
  • Learn about the inheritance of traits, specifically dominant and recessive alleles
  • Research how to calculate combined probabilities for independent events
  • Explore examples of genetic probability problems involving multiple traits
USEFUL FOR

This discussion is beneficial for students studying genetics, educators teaching probability in biology, and anyone interested in understanding the application of binomial expansion in genetic scenarios.

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Homework Statement



I'm stuck on a problem with two variables in it. The question wants to know what's the probability of getting 2 boys and 2 girls, with one of the boys being albino. They say one parent is albino and the other is a heterozygous carrier, so the change of getting it is 50% in the children.
So by binomial expansion, it's 1 4 6 4 1. I know the two girls and two boys is the middle term with 6(p^2)(q^2) but with q and p being getting a boy or girl at .50 each. But how do I encompass the albino probability in this? Multiply each child by .50?

Homework Equations



(p^4)+4(p^3)(q)+6(p^2)(q^2)+4(q)(p^3)+(q^4)

The Attempt at a Solution


I can easily find the probability of getting two girls and two boys, I would simply use the 6(p^2)(q^2) with p and q being .50 respectively. I just don't know how to factor in the albino part.
 
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Something like that. You should multiply with another binomial probability regarding the 4 children with "albino chromosome".
 
AGNuke said:
Something like that. You should multiply with another binomial probability regarding the 4 children with "albino chromosome".

It might be easier to calculate the probability that the two girls lack albinism and the probability that one of the boys has albinism.
 

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