In wheat plants kernel color is determined by three different genes each with two alleles. The more dominant alleles present,the darker the kernel color. If a plant with the genotype AaBbCc is crossed with another plant with the same genotype, what is the expected ratio of the darkest to lightest kernels? A) 1:64 B) 1:16 C) 1:4 D) 1:1

To determine the expected ratio of the darkest to lightest kernels when a plant with the genotype AaBbCc is crossed with another plant with the same genotype, we need to consider the inheritance of each gene separately and then combine the probabilities.<br /><br />Each gene has two alleles, and the more dominant alleles present, the darker the kernel color. Let's analyze each gene:<br /><br />1. Gene A: Aa<br /> - Possible combinations: AA, Aa, Aa, aa<br /> - Probability of having at least one dominant allele (A): 3/4<br /> - Probability of having no dominant alleles (aa): 1/4<br /><br />2. Gene B: Bb<br /> - Possible combinations: BB, Bb, Bb, bb<br /> - Probability of having at least one dominant allele (B): 3/4<br /> - Probability of having no dominant alleles (bb): 1/4<br /><br />3. Gene C: Cc<br /> - Possible combinations: CC, Cc, Cc, cc<br /> - Probability of having at least one dominant allele (C): 3/4<br /> - Probability of having no dominant alleles (cc): 1/4<br /><br />Now, let's calculate the probability of having the darkest kernel color, which means having at least one dominant allele from each gene:<br /><br />Probability of having the darkest kernel color = Probability of having at least one dominant allele from gene A * Probability of having at least one dominant allele from gene B * Probability of having at least one dominant allele from gene C<br />Probability of having the darkest kernel color = (3/4) * (3/4) * (3/4) = 27/64<br /><br />The probability of having the lightest kernel color, which means having no dominant alleles from each gene, is:<br /><br />Probability of having the lightest kernel color = Probability of having no dominant alleles from gene A * Probability of having no dominant alleles from gene B * Probability of having no dominant alleles from gene C<br />Probability of having the lightest kernel color = (1/4) * (1/4) * (1/4) = 1/64<br /><br />Therefore, the expected ratio of the darkest to lightest kernels is 27:1, which is closest to option B) $1:16$.