What is the probability that a descendent carries even at least one gene from the "Most Recent Common Ancestor"?

The human genome has only 20,000 protein-coding genes (which comprise 1-2% of human DNA). I'll be generous and use the 1% figure to assume that human DNA has about 2e6 "genes" (protein-coding or otherwise).

After 100 generations:

Probability any one gene comes from MRCA: 1/(2^100). Probability any one gene does not come from MRCA = 1 - 1/(2^100) Probability NO gemes come from MRCA = (1 - 1/(2^100))^(2^6) = 0.9999999999999999999999999999495129020658552444536494

Probability at least one gene comes from MRCA = 5.05 × 10^-29