Could you help me solve part B step-by-step? Given the answer 6ai: 3/16 and 6aii

Question

Could you help me solve part B step-by-step?

Given the answer 6ai: 3/16 and 6aii: 1/6.

I'm almost certain the answer is 1/72 but I have no idea how to solve the question.

Thank you!

6. The hypothetical genes A, B and C control production of a red pigment in a species of plant. For each gene there is a recessive ailele that gives rise to a non-functional protein. a. Assume that A, B and C act in a short biochemical pathway as follows: colorless ->orange --> yellow >red The alternative alleles that yield non-functioning products are designated a, b and c A pure-bred red-flowered plant is crossed with an aabbcc plant. The resulting Fi plants all have red flowers. You interbreed these Fi plants: i. What will be the proportion of F2 flowers that are orange? ii. If you backcross one of the orange F2 plants to the Fi, and grow a single Fs plant, what is the probability that it has white flowers?

Explanation / Answer

The pure bred red flower genotype will be AABBCC. When it's crossed with aabbcc plant, the the genotype of the all the F1 offspring will be AaBbCc, all with red pigmented flower.

now the genotype for a flower to be :

colorless: aa_____

Orange: A_bb__

Yellow: A_B_cc

Red: A_B_C_

1. when F1 progeny is interbred, I.e,., AaBbCc x AaBbCc

Thus, for the flower to be orange the proportion will be ( 3/4 x 1/4 ) =3/16

2. Now if we backcross the orange F2 plant with A_bb__ with AaBbCc

then the proportion of a plant to be colorless or white (aa) will be 1/4 as the proportion of white flowers will zero if the genotype is homozygous for AA in orange orange plant. Total no. of possible genotypic combinations in progenies will be 6x 8 =48

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