What is the probability that a cross between parents who are both homozygous recessive for trait will have offspring that are homozygous recessive for that trait?

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In the question, both parents are homozygous recessive for a trait. Therefore, the only genes present in each parent's genotype would be two copies of the recessive gene. 

If these parents decide to have offspring, 100% of their children will inherit two recessive alleles and will express the recessive trait.

An example of this can be demonstrated with the sickle cell anemia allele. If both parents have sickle cell anemia, then all of their offspring will have the disease phenotype. The disease phenotype of sickle cell anemia requires an individual to have two recessive alleles for sickle cell anemia. 

Another example is demonstrated with the trait of attached earlobes. Free ear lobes are a dominant trait which require only one dominant gene for the phenotype to appear. However, attached earlobes are a recessive trait. The only way the trait of attached earlobes will appear is if the person is homozygous recessive.  If both parents have attached earlobes, all of their offspring will have attached earlobes as well.

To summarize, recessive alleles will only appear in a phenotype when the individual is homozygous. If both parents are homozygous and recessive for a trait, 100% of their offspring will also express the trait.

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