If both parents have the right-handed gene, they will be right handed.
They are genetically right handed.
Not only that, but their children will be right handed. This is certain.
The children will be both right handed and genetically right handed.
If one parent does not carry the right handed gene (there is no LH gene), then that parent may or may not be right handed.
Genetically they are neutral.
Any offspring with one genetically right-handed parent have a 50% chance of inheriting the right handed gene, thus making the child both genetically right handed and right handed.
There is also a 50% chance that they will not inherit the right-handed gene (they inherit the genetic neutralness of one parent). If the child is genetically neutral, then that child has a 50% chance of behaving as a LH or RH person.
If both parents are genetically neutral, (50% chance that they show left or right handedness) there is a 100% chance that the offspring will be genetically neutral (meaning that they will definately not carry the right handed gene) and therefore a 50% chance that the children will either display left or right handedness.
It is interesting to note two things.
1) either parent missing the right-handed gene can give rise to handed neutral children indicates that the handedness gene is on the male chromosome.
2) All chimps (thus far checked) are right-handed.
If it is true that all chimps are indeed genetically right-handed, then this implies that the loss of this genetic information in Homo Sapiens Sapiens occured after the split from the common ancestor of Homo Barbarous (sp?). Infact, the prevelance of righthandedness in modern society indicaates that the loss of the righthanded gene is relatively recent (I would say in the last 25-30 thousand years or even more recently). It is now "epidemic". Within a relativlely few generations, genetically righthandedness will be in the minority, and then become extict from our species.