If a heterogeneous woman with traits for dark hair and freckles has a bay with a man with the same traits what is the chance their child would be born no freckles and light haired

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Answer:

The correct answer is [tex]\frac{1}{16}[/tex]  or zero, depending on the fathers genotype.

Explanation:

  • According to the question,
  1. dark hair phenotype is dominant over light hair.
  2. freckled phenotype is dominant over non-freckled phenotype.
  • Let for hairs, dominant allele be D and the recessive allele be d.
  • Let for freckles, dominant allele be F and the recessive allele be f.
  • According to the question, the mother is heterozygous for both the traits, that is, she has the genotype, DdFf and phenotype, dark hair and freckles.
  • But the father is said to have the same traits but not mentioned to be homozygous (DDFF) or heterozygous (DdFf).
  • If he is homozygous, then he would produce only DF gametes.
  • The mother produces the following gametes : DF, Df, dF, df.
  • On crossing homozygous father (DDFF) with heterozygous mother (DdFf), all the offspring will have  dark hair with freckles, so probability of obtaining a child with light hair and no freckles is zero.
  • If both the parents are heterozygous, DdFf,
  • Crossing them,

                                   DF             Df             dF            df

                     DF       DDFF         DDFf        DdFF        DdFf

                                 (D/F)           (D/F)         (D/F)         (D/F)

                     Df        DDFf           DDff         DdFf        Ddff

                                  (D/F)          (D/NF)       (D/F)        (D/NF)

                     dF        DdFF          DdFf        ddFF        ddFf

                                  (D/F)           (D/F)        (L/F)          (L/F)

                      df        DdFf            Ddff         ddFf         ddff

                                 (D/F)            (D/NF)      (L/F)          (L/NF)      

  • In the above cross, in the brackets (),
  1. D means dark hair.
  2. F means freckled.
  3. L means light hair.
  4. NF means non-freckled.
  • The phenotypes observed are :
  1. Dark hair with freckled  - 9.
  2. Dark hair with non-freckled - 3.
  3. Light hair with freckled -3.
  4. Light hair with non-freckled - 1.
  • Probability that a child born would be light haired with no freckles (ddff)  is  [tex]\frac{1}{16}[/tex].
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