Mendel needed to study two different genes rather than two different alleles of one gene to derive the principle of independent assortment because independent assortment is the phenomenon of the segregation of alleles of two or more genes during gamete formation independent of one another.
When Mendel studied the inheritance of two genes he observed that the alleles of these two genes were assorted during gamete formation in a random fashion and were not dependent on each other. He stated this as the law of independent assortment.
The independent assortment of genes is possible because of the random arrangement of homologous chromosomes at the metaphase plate during meiosis-I.
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