Final answer:
The most likely mode of inheritance if the trait displayed in the pedigree is rare and completely penetrant is autosomal recessive inheritance.
Step-by-step explanation:
If the trait displayed in the pedigree is rare and completely penetrant, the most likely mode of inheritance would be autosomal recessive inheritance.
This means that the trait is caused by a recessive allele on an autosome (non-sex chromosome).
In autosomal recessive inheritance, both parents must be carriers of the trait in order for their offspring to be affected.
Offspring have a 25 percent probability of being affected and a 75 percent probability of being unaffected.