Consider this mating between genotypes AaBBccDd and AabbCCDd, where A, B, C and D are loci that assort independently and the uppercase and lower case letter indicate the dominant allele and recessive allele respectively. Show all of your work.
a. What is the probability that any given offspring of this pair will be heterozygous at all loci?
b. What is the probability that an offspring will be homozygous at all four loci?
c. What is the probability that an offspring will be phenotypically dominant?

a. 1/4

b. 0

c. 9/16

Explanation:

Genotype of the parents: AaBBccDd and AabbCCDd.

Aa x Aa= 1/4 AA: 1/2 Aa: 1/4 aa

BB x bb= All Bb

cc X CC= All Cc

Dd x Dd= 1/4 DD: 1/2 Dd: 1/4 dd

a) The probability of the progeny heterozygous at all loci= 1/2 Aa x 1 Bb x 1 Cc x 1/2 Dd = 1/4.

b) The probability of an offspring that is homozygous at all four loci= 0

Since the progeny will be heterozygous for B and C. None of the progeny can be homozygous at these two loci.  

c.  

Aa x Aa= 3/4 dominant: 1/4 recessive

BB x bb= All dominant

cc X CC= All dominant

Dd x Dd=  3/4 dominant: 1/4 recessive

The probability of dominant offspring= 3/4 x 3/4 = 9/16

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