Gamete Formation

In this dioecious plant system:

• The female parent (genotype $XX$) produces egg cells with the genotype $X$.
• The male parent (genotype $XY$) produces two types of sperm cells through meiosis: $X$ sperm (50% probability) and $Y$ sperm (50% probability).

Double Fertilization Process

Double fertilization involves two fusion events:

• Embryo Formation: An egg cell ($X$) fuses with one sperm cell ($X$ or $Y$).
• Endosperm Formation: The central cell (formed from two polar nuclei, which are derived from the female parent, hence $XX$) fuses with the other sperm cell ($X$ or $Y$). The endosperm is typically triploid (3n).

Genotype Outcomes

Based on the type of sperm involved:

• Scenario 1: Fertilization by $X$ sperm (50% probability)
  • Embryo: $X$ (egg) + $X$ (sperm) = $XX$
  • Endosperm: $XX$ (central cell) + $X$ (sperm) = $XXX$
• Scenario 2: Fertilization by $Y$ sperm (50% probability)
  • Embryo: $X$ (egg) + $Y$ (sperm) = $XY$
  • Endosperm: $XX$ (central cell) + $Y$ (sperm) = $XXY$

Final Result

Therefore, after double fertilization, 50% of the ovules will develop embryos with genotype $XX$ and endosperms with genotype $XXX$. The other 50% will develop embryos with genotype $XY$ and endosperms with genotype $XXY$.

This matches the outcome described as: 50% ovules will have $XXX$ endosperm and $XX$ embryo, while the other 50% will have $XXY$ endosperm and $XY$ embryo.