Mendel claimed that transmission from parent to offspring of alleles of a given gene is independent for each gene and its alleles. What does this mean?

Any gamete that one allele of a gene gets separated into is equally likely to contain a dominant or recessive allele for the other gene.

Explanation:

Gregor Mendel, in his experiments had initially stated that the alleles of a gene separate into gametes in his law of segregation. However, this law portrays how a single gene responsible for a single trait is passed on.

When Mendel performed a dihybrid cross i. e. one involving two traits encoded by two different genes, he came up with the principle that the alleles of one gene gets sorted into gametes independently of one another i. e. the allele received by an organism for one gene does not affect the reception of the alleles for the other gene.

He discovered this when he crossed a pea plant and observed the seed shape and seed colour in it. He crossed a homozygous round yellow (RRYY) pea and a homozygous green wrinkled (rryy) pea to produce an all round yellow offspring (RrYy) in the F1 generation. He then self-crossed this dihybrid plant to get an expected ratio of 9:3:3:1 with four distinct phenotypes. This shows that each allele of the seed shape gene separated without affecting the separation of the alleles of the seed colour gene i. e. every possible combination of alleles for each gene is likely to occur.