In cucumbers, dull fruit (d) is dominant over glossy fruit (d), orange fruit (r) is dominant over cream fruit (r), and bitter cotyledons (b) are dominant over nonbitter cotyledons (b). the three characters are encoded by genes located on different pairs of chromosomes. a plant homozygous for dull, orange fruit and bitter cotyledons is crossed with a plant that has glossy, cream fruit and nonbitter cotyledons. an f1 plant is crossed with a plant that has glossy, cream fruit and nonbitter cotyledons. give the expected proportions among the progeny of this cross with a glossy, cream, bitter phenotype

To solve we must first name all alleles:
Dull fruit (D)
Glossy fruit (d)
Orange fruit (R)
Cream fruit (r)
Bitter cotyledons (B)
Nonbitter cotyledons (b)

So our cross would be:
DDRRBB x ddrrbb

and since each parent is homozygous (one dominant and one recessive) the resulting F1 would be 100% heterozygous for all characters.

The F1 parents, according to the problem, would then be:
DdRrBb x ddrrbb

So here we should solve each character separately and establish each genotype's probability from happening from the probability of an already calculated genotype. Here's how it works:

Dd x dd would result in 50% Dd and 50% dd (we only care about the recessive homozygous because is the one asked in the problem)

Rr x rr would result in 50% Rr and 50% rr
and if we part from the fact there is only 50% chance of dd happening (not 100%), we obtain that there is 25% chance for ddRr and 25% chance for ddrr (again, we only care about the recessive homozygous).

Bb x bb would result in 50% Bb and 50% bb
parting from ddrr 25%, we obtain a 12,5% for ddrrBb and 12,5% for ddrrbb, and the last one is the answer to the problem.

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