Final answer:
The progeny from a cross between a heterozygous tall/smooth plant and a homozygous short/wrinkled plant that are homozygous for short and wrinkled alleles would be 1/4.
Step-by-step explanation:
The question asks us to determine the proportion of progeny that is homozygous for short and wrinkled alleles from a cross between an F1 plant with heterozygous tall and smooth alleles (TtSs) and a homozygous short/wrinkled plant (ttss).
Given that smooth seeds (S) are dominant to wrinkled seeds (s), and tall plants (T) are dominant to short plants (t), the cross would be between TtSs x ttss.
Using Punnett squares or the product rule, we know the genotype for height would have a 1:1 ratio of short (t) to tall (T) alleles and the same for seed texture. The offspring that are homozygous for short and wrinkled alleles would therefore be represented by ttss.
Since each trait has a 1:1 ratio, we can calculate the probability of ttss offspring as (1/2) for short stature multiplied by (1/2) for wrinkled seeds, which equals (1/4).