What is the chance a given gene will end up in a given gamete?
A cell contains two haplotypes (or two set of all chromosomes). One haplotype inherited from the mother, one from the father. A haploid cell, resulting from meiosis, will receive either the maternal (or grandmother if you prefer) or paternal (or grandfather if you prefer) haplotype. It cannot receive anything else. Hence the probably must be 0.5 (or 50%).

Note that you are using the term "gene" incorrectly. You should use the term "allele" instead. And while you are improving your genetic vocabulary you should also check the term "locus". Also, the term "desired gene" is never used. We talk about "beneficial allele" or "detrimental allele".