Let us say a germ cell had a desired allele. This germ cell was replicated during interphase so that it had two of the desired allele. It then underwent meiosis.
My question then is, what is the chance a given allele will end up in a given gamete that will be involved in conception?
Firstly, there is a 50% chance a chromosome will be assigned to a given daughter cell. This is because of independent assortment. In addition, cross over occurs at chiasmata. Lets assume then that there was a 50% chance that an allele will be crossed over (although this probability may be far from true)
The process during meiosis is that cross-over occurs first. We have two desired alleles, each on one of two pairs of chromatid attached to each other. There is 50% chance for a given allele to cross over. For example, the chance for both desired alleles to cross over is 1/4 (1/2 x 1/2), the chance only one will cross over is 2/4 (since either of the two desired alleles can cross over).
Then there is the first independent assortment during meiosis I which produces the desired daughter cell. In this case there is a 50% chance that a given chromatid pair (containing the desired allele) will be assigned to the desired daughter cell. However, in the case where a desired allele is found in both homologs (2/4 of a chance), then the chance that at least one desired allele will be in the daughter cell is 100%.
Finally, during meiosis II, another independent assortment occurs which produces the desired gamete. The same rule applies with a 50% chance a given allele will be assigned to a given cell (in this case the gamete). However, if the desired daughter cell contains two of the desired alleles, then there is a 100% chance that the cell will have the desired allele.
In conclusion, the chance I estimated that the gamete will have at least one desired allele is 50%. Although, I'm not sure if this is correct. Anyone mind confirming this.