In a standard Mendelian dihybrid cross, the F2 generation produces 16 possible genotype combinations in a 9:3:3:1 phenotypic ratio. Among these, the pure homozygous offsprings (both traits pure dominant or pure recessive, like YYRR, yyrr, YYrr, yyRR) total 4 out of 16, which simplifies to 1/4.