State the Law of Independent Assortment and explain how it is derived.

(A) The Law of Independent Assortment states that when two pairs of traits are combined in a hybrid,the segregation of one pair of characters is independent of the other pair of characters during gamete formation.
These characters are randomly rearranged in the offspring,producing both parental and new combinations of traits.
In a dihybrid cross,the phenotypes (round yellow,wrinkled yellow,round green,and wrinkled green) appeared in a ratio of $9:3:3:1$.
This ratio was observed for several pairs of characters studied by Mendel.
The ratio of $9:3:3:1$ can be derived as a combination of the monohybrid ratios: $(3 \text{ round} : 1 \text{ wrinkled}) \times (3 \text{ yellow} : 1 \text{ green}) = 9 \text{ round yellow} : 3 \text{ wrinkled yellow} : 3 \text{ round green} : 1 \text{ wrinkled green}$.
Based on these observations of dihybrid crosses,Mendel proposed the Law of Independent Assortment.
The Punnett Square is used to understand the independent segregation of two pairs of genes during meiosis in an $F_1$ $RrYy$ plant.
During segregation,$50\%$ of the gametes receive the gene $R$ and $50\%$ receive $r$. Similarly,$50\%$ receive $Y$ and $50\%$ receive $y$.
Since the segregation of the $R/r$ pair is independent of the $Y/y$ pair,each gamete has a $25\%$ $(1/4)$ probability of being $RY$,$Ry$,$rY$,or $ry$.
By placing these four types of gametes on the axes of a Punnett Square,one can easily derive the genotypes of the $F_2$ generation.