If an individual is 94% of a particular ethnicity, how many generations back would the ancestor be 100% of that ethnicity?

Question

I know this is unscientific, but I'm trying to reverse engineer my calculations based on the percentage of DNA inherited from a parent(2).  The average DNA inheritance pattern is 50% (parents) - > 25% (grandparent) - > 12.5% (great-grandparent) - > 6.25% (great-great grandparent).  So, if I start at 94% (me) Irish - > 47% (=parent) - > 23.5% (=grandparent) - > 11.75% (=great-grandparent) - > 5.875 (=great-great grandparent).  I'm assuming that is levels out by the great-grandparent?  

Answer 1

You had it right for the first half.  If the person gets 50% from a parent with the trait and a parent without the trait, then the next generation will get 25% (presuming the other parent does not carry the trait), and the next generation will get 12.5%, and the next generation will get 6.25%, and the next generation will get 3.125% which is basically equal to 3%.

This analysis assumes that crossover does not alter or eliminate the gene/genes in any generation.