Allele ‘A’ is dominant over allele ‘a’ and results in dark skin pigmentation. In a mating of Aa with Aa, if 6
offspring are produced, the probability of all having dark pigment is:
(1) 0.18
(2) 0.75
(3) 0.24
(4)0.12
Probability of Dark Skin Pigmentation in Genetic Cross: Understanding Allele Inheritance
In genetics, understanding how traits like skin pigmentation are inherited is essential. In this scenario, we’re examining a genetic cross between two individuals who both carry the heterozygous genotype Aa. The A allele is dominant and leads to dark skin pigmentation, while the a allele is recessive.
The question is:
If two individuals with genotype Aa mate and produce 6 offspring, what is the probability that all of the offspring will have dark skin pigmentation?
Genotype and Phenotype Overview
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Allele A: Dominant, leading to dark skin pigmentation.
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Allele a: Recessive, leading to lighter skin pigmentation.
In a mating of Aa × Aa, the following possibilities exist for the offspring:
| Parent 1 | A | a |
|---|---|---|
| Parent 2 | A | AA |
| a | Aa |
Resulting Genotypes:
-
AA: Homozygous dominant (dark skin)
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Aa: Heterozygous (dark skin)
-
aa: Homozygous recessive (light skin)
Thus, the offspring have the following probabilities for skin pigmentation:
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AA or Aa → Dark skin pigmentation
-
aa → Light skin pigmentation
Probabilities of Each Genotype
From a cross of Aa × Aa, the possible genotype outcomes are:
-
AA (Dark skin) → 1/4 probability
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Aa (Dark skin) → 2/4 (or 1/2) probability
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aa (Light skin) → 1/4 probability
Therefore, the total probability of an offspring having dark skin (either AA or Aa) is:
-
P(Dark skin) = P(AA) + P(Aa) = 1/4 + 2/4 = 3/4
Calculating the Probability for All Offspring to Have Dark Skin
Now, we need to calculate the probability that all 6 offspring will have dark skin pigmentation. Since the probability of any one offspring having dark skin is 3/4, the probability for all 6 offspring to have dark skin is:
(3/4)6=0.177
So, the probability of all 6 offspring having dark skin is approximately 0.18.
Answer
The correct answer is (1) 0.18.
Key Takeaways
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Mendelian inheritance helps us understand how traits are passed down from parents to offspring. In this case, dark skin pigmentation is governed by a dominant allele (A).
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The probability of all offspring inheriting dark skin in this genetic cross can be calculated by raising the probability of an individual offspring having dark skin to the power of the number of offspring.
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The result of 0.18 shows that while the chances are good for dark skin pigmentation, it’s not guaranteed that all offspring will have dark skin.
Final Thoughts
Genetics can sometimes feel complex, but breaking down the probability of inheriting specific traits can be done easily using Mendel’s laws of inheritance. Understanding dominant and recessive alleles is crucial for predicting outcomes in offspring, whether it’s for skin pigmentation or other traits. In this case, the chance of all 6 offspring inheriting dark skin is about 18%.
