Final answer:
The child of Darnell and Tinaka might have inherited the autosomal recessive disorder despite genetic precautions possibly due to an inaccurate genetic test or a new mutation, while incomplete penetrance and variable expressivity are unlikely explanations.
Step-by-step explanation:
When Darnell and Tinaka, who are both carriers of an autosomal recessive disorder, have a child using preimplantation genetic diagnosis, there is a 25% probability that their child will inherit the disease if it's a disorder like Tay-Sachs disease or cystic fibrosis.
However, it seems that their child unfortunately has the disorder despite the measure taken. A possible scientific explanation for this outcome could be a) The genetic test was inaccurate, meaning that the preimplantation genetic diagnosis failed to detect the presence of the defective genes accurately. Another explanation b) Incomplete penetrance, is not a likely scenario in this case as it refers to individuals who carry the disease allele but do not express the disorder, which doesn't apply to lethal recessive disorders that are typically fully penetrant if the child inherits two copies of the allele.
Likewise, c) Variable expressivity is also unlikely as it refers to the range of signs and symptoms that can occur in different people with the same genetic condition and would not cause a child without the genetic condition to suddenly develop it. Hence, another explanation d) There was a new mutation in the embryo is also possible, but it would be rare for a new mutation to mimic an existing genetic condition precisely.