When Mendel self-pollinated plants from the purple-flowered F1 generation, he saw that one out of every four plants in the F2 had white flowers. What reasoning did Mendel use to explain how the white, hidden trait reappeared?

The reasoning that Mendel uses to explain how the white hidden trait reappeared was that only offsprings that have two recessive alleles show the hidden trait.

Explanation:

The F1 generation had two different alleles, one that coded for purples flowers and one that coded for white flowers, the allele for white flowers was hidden by the dominant allele, that is why the F1 generation were purple flowers. In the F2 generation, the two alleles that coded for flower color were the same, which means that they were both recessive and, as a result, the F2 generation of flowers was white because there was not a dominant allele that hid the other one.