When an organism of genotype AaBbCc produces gametes, what proportion will be Abc, AbC, ABC, abc, abC, aBc. Assuming there is incomplete dominance across all three genes, what would be the proportion of phenotypes that will not be intermediates?
There are actually eight potential gamete types your organism can produce: ABC, ABc, AbC, aBC, Abc, aBc, abC, and abc. The chances of any of these being in any given egg or sperm cell is exactly the same-- 1/8, or 12.5% (assuming they randomly assorted, and are not located on the same chromosome).
In order to talk about incomplete dominance and the chances of a particular type of phenotype, we have to talk about the actual offspring produced. This requires another parent. If we assume the other parent also is of AaBbCc genotype, that parent produces the same type of gametes listed above. Creating a Punnett square for crossing these two will give us the eight choices listed in the first paragraph on both the top and the side of the Punnett square. In order for there NOT to be any intermediates, the offspring will have to be either AABBCC, or aabbcc. There is 1/64 chance of either of these happening (one square of the 64 possible will have AABBCC, and one will have aabbcc). The chance of there being no intermediate phenotype is the chance of either of these--2/64, or 1/32. This is a percentage of 3.1%. In sum, 97% of the offspring of a cross between two parents of genotype AaBbCc will show an intermediate phenotype in one or more traits, and 3% will show either all three dominant or all three recessive traits.