Question

a dihybrid cross is created from plants that are heterozygous for both round seeds and yellow seed color. what is the ratio of offspring that have round seeds and yellow seed color? 1:16 3:16 9:16 16:16

Explanation:

Step1: Determine the genotypes of the parents

Let \(R\) represent the allele for round seeds (dominant) and \(r\) for wrinkled seeds (recessive). Let \(Y\) represent the allele for yellow seeds (dominant) and \(y\) for green seeds (recessive). The parents are heterozygous for both traits, so their genotype is \(RrYy\).

Step2: Use the Punnett square or the multiplication rule

For a single - trait cross (\(Rr\times Rr\)):
The probability of getting a round - seeded offspring (\(RR\) or \(Rr\)) is \(P(R\_)=\frac{3}{4}\) (using the formula \(P(RR)+P(Rr)=\frac{1}{4}+\frac{2}{4}\)).
For a single - trait cross (\(Yy\times Yy\)):
The probability of getting a yellow - seeded offspring (\(YY\) or \(Yy\)) is \(P(Y\_)=\frac{3}{4}\) (using the formula \(P(YY)+P(Yy)=\frac{1}{4}+\frac{2}{4}\)).

Step3: Use the multiplication rule for independent events

Since seed shape and seed color are independent traits (Mendel's law of independent assortment), the probability of an offspring having both round seeds (\(R\_\)) and yellow seeds (\(Y\_\)) is \(P(R\_\cap Y\_)=P(R\_)\times P(Y\_)\).
Substitute \(P(R\_)=\frac{3}{4}\) and \(P(Y\_)=\frac{3}{4}\) into the formula: \(P(R\_\cap Y\_)=\frac{3}{4}\times\frac{3}{4}=\frac{9}{16}\)

Answer:

C. \(9:16\)