When crossing an organism that is homozygous recessive for a single trait (aa) with a heterozygote (aa), what is the chance of producing an offspring with the homozygous recessive phenotype?

50%

Explanation:

if homozygous recessive for a single trait (aa) cross with heterozygote (Aa)

i.e Aa ×  aa

there F1 offspring will be:

the test cross is show below

           A          a

a          Aa        aa

a          Aa         aa

=(Aa, Aa, aa, aa)

the results shows 50% heterozygote and 50% homozygous recessive phenotype.