Question

practice with probability
in corn plants, the gene for yellow kernel color (y) is dominant over the gene for white kernel color
(y), and the gene for plant height (t) is dominant over the gene for dwarfness (t).
a heterozygous yellow - kernel, tall corn plant (yytt) is crossed with a heterozygous yellow - kernel,
tall corn plant (yytt).
use the results of the punnett squares below to answer the question.
what is the phenotypic frequency of dwarf, white corn
offspring (yytt)?
9/16
1/16
3/16

Explanation:

Step1: Determine the probability of getting 'yy'

For the kernel color gene, when crossing \(Yy\times Yy\) (as shown in the Punnett - square for kernel color), the probability of getting \(yy\) (white kernel) is \(\frac{1}{4}\). This is because in the \(Yy\times Yy\) cross, the genotypes are \(YY:Yy:Yy:yy\) (1:2:1 ratio).

Step2: Determine the probability of getting 'tt'

For the plant - height gene, when crossing \(Tt\times Tt\) (assuming a similar independent - assortment and Mendelian cross as for the color gene, since the problem is about a di - hybrid cross \(YyTt\times YyTt\)), the probability of getting \(tt\) (dwarf) is \(\frac{1}{4}\). In a \(Tt\times Tt\) cross, the genotypes are \(TT:Tt:Tt:tt\) (1:2:1 ratio).

Step3: Use the multiplication rule for independent events

Since the inheritance of kernel color and plant height are independent events (Mendel's law of independent assortment), the probability of getting \(yytt\) (dwarf, white corn) is the product of the probability of getting \(yy\) and the probability of getting \(tt\).

$$P(yytt)=P(yy)\times P(tt)=\frac{1}{4}\times\frac{1}{4}$$

Answer:

\(\frac{1}{16}\)