The following F2 results occur from a dihybrid cross (AaBb x AaBb): purple: A_B_ 9/16 white: aaB_ 3/16 white: A_bb 3/16 white: aabb 1/16 If a double heterozygote (AaBb) is crossed with a fully recessive organism (aabb), what phenotypic ratio is expected in the offspring? a. 3 (purple) : 1(white)b. 3 (whilte) : 1(purple)c. 1(purple): 1(white)d. 9 (purple): 1(white) I know the answer is B but I want to know why. Please provide a good explanation for a good rating.

b. 3 (whilte) : 1(purple)

Explanation:

The first dihybrid crossing is between AaBb x AaBb

Now, if the double heterozygous traits self crossed, we have the following gametes shown below for the F₂ crossing.

AaBb = (AB, Ab, aB, ab)

                    AB                     Ab                     aB                     ab

AB                AABB                AABb                AaBB                AaBb

Ab                AABb                AAbb                AaBb                Aabb

aB                AaBB                 AaBb                aaBB                aaBb

ab                AaBb                 Aabb                 aaBb                aabb

We were being told that the results are;

purple: A_B_ 9/16

white: aaB_ 3/16

white: A_bb 3/16

white: aabb 1/16

From above, we can see that the same is true;

For Purple color; we Have (AABB and AaBb) since A is dominant to a and B is dominant to b.

∴ From the above punnet square; we have 9 purple colors which are:

(AABB, AABb, AaBB, AaBb, AABb, AaBb, AaBB, AaBb, AaBb) = 9/16

white: aaB_ ( since B is dominant to b, it can be either BB or Bb)

= (aaBB, aaBb, aaBb) = 3/16

white: A_bb ( since A is dominant to a, it can be either AA or Aa)

= (AAbb, Aabb, Aabb) = 3/16

white: aabb i.e homozygous recessive = (aabb) = 1/16

Furthermore, the question goes further by saying:

If a double heterozygote (AaBb) is crossed with a fully recessive organism (aabb), what phenotypic ratio is expected in the offspring?

If AaBb self crossed, we have:  (AB, Ab, aB, ab)

If aabb self crossed, we have: (ab, ab, ab, ab)

                    AB                     Ab                     aB                     ab

ab                AaBb                Aabb                aaBb                 aabb

ab                AaBb                Aabb                aaBb                 aabb

ab                AaBb                 Aabb               aaBb                 aabb

ab                AaBb                 Aabb                aaBb                aabb

AaBb ( purple)

= 4/16

= 1/4

= 0.25

= 25%

Aabb (white)

= 4/16

= 1/4

= 0.25

= 25%

aaBb (white)

= 4/16

= 1/4

= 0.25

= 25%

aabb (white)

= 4/16

= 1/4

= 0.25

= 25%

Now the proportion of white to purple =  (25%+25%+25%): 25%

=  75%:25%

= 3(white):1(purple)

We can therefore conclude that the expected phenotypic ratio in the cross between a double heterozygote (AaBb) with a fully recessive organism (aabb) yeids;

3 (whilte) : 1(purple)