Explain the Law of Independent Assortment based on a dihybrid cross.

(N/A) The Law of Independent Assortment states that when two pairs of traits are combined in a hybrid,segregation of one pair of characters is independent of the other pair of characters.
In a dihybrid cross,the phenotypic ratio of round-yellow,round-green,wrinkled-yellow,and wrinkled-green seeds was observed as $9:3:3:1$. This ratio can be derived as a combination of $3$ yellow : $1$ green and $3$ round : $1$ wrinkled.
This can be expressed as: $(3 \text{ Round} : 1 \text{ Wrinkled}) \times (3 \text{ Yellow} : 1 \text{ Green}) = 9 \text{ Round-Yellow} : 3 \text{ Round-Green} : 3 \text{ Wrinkled-Yellow} : 1 \text{ Wrinkled-Green}$.
Based on the results of the dihybrid cross,Mendel proposed the Law of Independent Assortment.
In the $F_1$ generation $(RrYy)$,the independent segregation of two pairs of genes can be understood using a Punnett square.
During gamete formation,$50\%$ of the gametes carry the $R$ allele and $50\%$ carry the $r$ allele. Similarly,$50\%$ of the gametes carry the $Y$ allele and $50\%$ carry the $y$ allele. Because segregation is independent,four types of gametes are produced in equal proportions: $RY, Ry, rY, ry$ (each with a probability of $1/4$).
By placing these gametes on the axes of a Punnett square,we obtain $16$ combinations in the $F_2$ generation.
The phenotypic ratio is $9:3:3:1$ (Round-Yellow : Round-Green : Wrinkled-Yellow : Wrinkled-Green).
The genotypic ratio is $1:2:2:4:1:2:1:2:1$.