The answer: 0.25% of genes will be different
How I got the answer is by simulating two genomes using the following code:
lengthGenome=3234.83*10^6
numGenes=19000
lengthGene=3000
fracSim=0.999
trialHolder=1:100
for(trial in 1:100){
genomeA=rep(0,lengthGenome)
genomeB=rep(0,lengthGenome)
genomeA[sample(1:lengthGenome,round((1-fracSim)*lengthGenome))]=1
genomeB[sample(1:lengthGenome,round((1-fracSim)*lengthGenome))]=1
startGenes=sample(1:lengthGenome,numGenes)
equalGene=0
for(i in 1:numGenes){
equalGene=all(genomeA[startGenes[i]:(startGenes[i]+lengthGene)]==genomeB[startGenes[i]:(startGenes[i]+lengthGene)])+equalGene
}
trialHolder[trial]=equalGene/numGenes
}
print(mean(trialHolder))
To quickly walk through the code you make a genome of the specified length, and then change 0.01% of the genome to be a mutation, and therefore not similar to the other genome at the same position. Then define the start points of the number of genes specified. For each gene region, see if the genes look exactly the same (if one does not have the mutation within). Finally just track the proportion of genes that are all equal.
I ran the code 100 times and averaged the result, it took a little while. There is likely a more direct, probabilistic way to do this but I imagine the result would be the same.