Q. Raj having genotype AaBBCc for skin colour marries Simran having genotype AAbbCc for skin colour. What is the chance that they have a child whose skin colour does not match with either Raj's or Simran's?
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Solution:
Inheritance of skin colour is polygenic. Three different genes colour this trait. The more number of dominant alleles a person has the darker is his skin. Raj has genotype AaBBCc with 4 dominant alleles. He will produce four types of gametes ABC, ABc, aBC, and aBc. Simran has genotype AAbbCc with 3 dominant alleles. She will produce two types of gametes AbC and Abc. Simran is fairer than Raj. The genotypes of their children can be tabulated as follows:
ABC ABc aBC aBc AbC AABbCC
5 dominant alleles Darker than Raj and Simran AABbCc
4 dominant alleles Same skin tone as that of Raj AaBbCC
4 dominant alleles Same skin tone as that of Raj AaBbCc
3 dominant alleles Same skin tone as that of Simran Abc AABbCc
4 dominant alleles Same skin tone as that of Raj AABbcc
3 dominant alleles Same skin tone as that of Simran AaBbCc
3 dominant alleles Same skin tone as that of Simran AaBbcc
2 dominant alleles Fairer than Raj and Simran
Thus two genotypes AABbCC and AaBbcc out of 8 genotypes whose skin colour doesn't match with either Raj's or Simran's. Their probability is $\frac{2}{8} \, = \, 25\%$
| ABC | ABc | aBC | aBc | |
| AbC | AABbCC 5 dominant alleles Darker than Raj and Simran | AABbCc 4 dominant alleles Same skin tone as that of Raj | AaBbCC 4 dominant alleles Same skin tone as that of Raj | AaBbCc 3 dominant alleles Same skin tone as that of Simran |
| Abc | AABbCc 4 dominant alleles Same skin tone as that of Raj | AABbcc 3 dominant alleles Same skin tone as that of Simran | AaBbCc 3 dominant alleles Same skin tone as that of Simran | AaBbcc 2 dominant alleles Fairer than Raj and Simran |