Mutated Offspring

An animal appears normal if it has two normal genes or one normal and one mutated gene. If it has two mutated genes, it appears mutated. Any given animal has a 50% chance to contribute either of its genes to its offspring.

Animals $A$ and $B$ are parents of $C$ and $D$. $C$ and $D$ are parents of $E$. $A$ and $B$ both have one normal and one mutated gene. We know $C$ and $D$ both appear normal.

What is the probability that $D$ has one normal and one mutated gene given that $E$ appears normal?