In peas, tall (T) is dominant over dwarf (t), yellow (Y) is dominant over green (y) and smooth is dominant (S) over wrinkled (s). What fraction of the offspring in the following cross would be homozygous recessive for all gene pairs in the cross: YyTtSs × Yyttss?

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Question: In peas, tall (T) is dominant over dwarf (t), yellow (Y) is dominant over green (y) and smooth is dominant (S) over wrinkled (s). What fraction of the offspring in the following cross would be homozygous recessive for all gene pairs in the cross: YyTtSs × Yyttss?

To solve this genetics question, we need to find what fraction of the offspring will be homozygous recessive for all three traits, that is: yy tt ss

Let us carefully break down the cross YyTtSs × Yyttss, step by step for each gene.

Step 1: Determine the gametes for each gene pair

We look at each gene separately and find out how often the homozygous recessive genotype will appear.

Gene 1: Yy × Yy

Cross: Yy × Yy

Possible genotypes: YY, Yy, yY, yy
Probability of yy = 1/4

Gene 2: Tt × tt

Cross: Tt × tt

Possible genotypes: Tt, tt
Probability of tt = 1/2

Gene 3: Ss × ss

Cross: Ss × ss

Possible genotypes: Ss, ss
Probability of ss = 1/2

Step 2: Multiply probabilities

Now multiply the probabilities of all three homozygous recessive genotypes to get the total fraction of offspring that are yy tt ss:

1/4 yy × 1/2 tt × 1/2 ss = 1/16 yyttss

1 out of 16 offspring will be homozygous recessive (yy tt ss) for all three gene pairs.

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