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Tetrahybrid cross: probabilities of genotypes

The genotype of F1 individuals in a tetrahybrid cross is AaBbCcDd. Assuming independent assortment of these four genes, what are the probabilities that F2 offspring will have the following genotypes?
a)aabbccdd
b)AaBbCcDd
c)AABBCCDD
d)AaBBCcDd
e)AaBBCCdd

Please help me on tackling problems like this in a systematic way.

Solution Preview

Please see attached file where formatting is conserved.
If you do not have to list the alleles in your answers, this would be a better and easier way to calculate the probabilities.

The genotype of F1 individuals in a tetrahybrid cross is AaBbCcDd.  Assuming independent assortment of these four genes, what are the probabilities that F2 offspring will have the following genotypes?
a)aabbccdd
b)AaBbCcDd
c)AABBCCDD
d)AaBBccDd
e)AaBBCCdd

We have four groups

A
Parent 1 Parent 2
A A
a a

Possible combinations
A A
A a
a A
a a

Thus there is a total of 4 combinations

B
Parent 1 Parent 2
B B
b b

Possible combinations
B B
B b
b B
b b

Thus there is a total of 4 combinations

C
Parent 1 Parent 2
C C
c c

Possible combinations
C C
C c
c C
c c

Thus there is a total of 4 combinations

D
Parent 1 Parent 2
D D
d d

Possible combinations
D D
D d
d D
d d

Thus there is a total of 4 combinations

A genotype has the 4 groups together
Therefore possible number of ways of forming the genotype = 4 x 4 x 4 x 4= 256

Probability is the number of ways in which the desired ...

Solution Summary

The solution calculates the probabilities of F2 offspring having the stated genotypes.

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