Two genes assort independently. The allele $a$ in the homozygous state ($aa$) makes the plant white whatever the other gene is. A plant with at least one $A$ is black if it has at least one $B$, and brown if it is $bb$. Two plants of genotype $AaBb$ are crossed. One black plant of the offspring is chosen at random and test crossed with an $aabb$ plant. What fraction of the test cross progeny is expected to be brown?