Answer :
To find the ratio of the offspring that will have round and yellow seeds from the cross of two plants with genotype RrYy, we need to consider the inheritance of each trait separately.
1. Determine all possible combinations of genotypes for the offspring:
Each parent can produce the following gametes:
- For the "R" gene: R or r
- For the "Y" gene: Y or y
Thus, each parent can produce four types of gametes due to the independent assortment:
`RY, Ry, rY, ry`
We can combine these gametes to form the genotypes of the offspring. There are 16 possible combinations from the cross of the two RrYy parents:
[tex]\[ \begin{aligned} &RY \times \{ RY, Ry, rY, ry \} \\ &Ry \times \{ RY, Ry, rY, ry \} \\ &rY \times \{ RY, Ry, rY, ry \} \\ &ry \times \{ RY, Ry, rY, ry \} \\ \end{aligned} \][/tex]
Combining these gametes, the 16 possible genotypes are:
[tex]\[ \begin{aligned} & \text{RRYY, RRYy, RrYY, RrYy,} \\ & \text{RRYy, RRyy, RrYy, Rryy,} \\ & \text{RrYY, RrYy, rrYY, rrYy,} \\ & \text{RrYy, Rryy, rrYy, rryy} \\ \end{aligned} \][/tex]
2. Determine the phenotypes for round and yellow seed combinations:
For a seed to be round, it must have at least one dominant "R" allele (R_).
For a seed to be yellow, it must have at least one dominant "Y" allele (Y_).
Checking the above combinations, the phenotypes for round and yellow seeds are:
[tex]\[ \begin{aligned} & \text{RRYY} \rightarrow \text{Round and Yellow} \\ & \text{RRYy} \rightarrow \text{Round and Yellow} \\ & \text{RrYY} \rightarrow \text{Round and Yellow} \\ & \text{RrYy} \rightarrow \text{Round and Yellow} \\ \end{aligned} \][/tex]
Only these four combinations result in round and yellow seeds.
3. Count the number of times the "Round and Yellow" phenotype occurs out of the total combinations:
[tex]\[ \frac{\text{Number of "Round and Yellow" phenotypes}}{\text{Total number of combinations}} = \frac{4}{16} \][/tex]
Therefore, the ratio of offspring that will have round and yellow seeds is [tex]\( \frac{4}{16} \)[/tex], which simplifies to:
[tex]\[ 4:16 \][/tex]
Therefore, considering the given options, the ratio [tex]\( 4:16 \)[/tex] is indeed the correct answer. Among the provided options, this corresponds to [tex]\( \boxed{4:16} \)[/tex].
1. Determine all possible combinations of genotypes for the offspring:
Each parent can produce the following gametes:
- For the "R" gene: R or r
- For the "Y" gene: Y or y
Thus, each parent can produce four types of gametes due to the independent assortment:
`RY, Ry, rY, ry`
We can combine these gametes to form the genotypes of the offspring. There are 16 possible combinations from the cross of the two RrYy parents:
[tex]\[ \begin{aligned} &RY \times \{ RY, Ry, rY, ry \} \\ &Ry \times \{ RY, Ry, rY, ry \} \\ &rY \times \{ RY, Ry, rY, ry \} \\ &ry \times \{ RY, Ry, rY, ry \} \\ \end{aligned} \][/tex]
Combining these gametes, the 16 possible genotypes are:
[tex]\[ \begin{aligned} & \text{RRYY, RRYy, RrYY, RrYy,} \\ & \text{RRYy, RRyy, RrYy, Rryy,} \\ & \text{RrYY, RrYy, rrYY, rrYy,} \\ & \text{RrYy, Rryy, rrYy, rryy} \\ \end{aligned} \][/tex]
2. Determine the phenotypes for round and yellow seed combinations:
For a seed to be round, it must have at least one dominant "R" allele (R_).
For a seed to be yellow, it must have at least one dominant "Y" allele (Y_).
Checking the above combinations, the phenotypes for round and yellow seeds are:
[tex]\[ \begin{aligned} & \text{RRYY} \rightarrow \text{Round and Yellow} \\ & \text{RRYy} \rightarrow \text{Round and Yellow} \\ & \text{RrYY} \rightarrow \text{Round and Yellow} \\ & \text{RrYy} \rightarrow \text{Round and Yellow} \\ \end{aligned} \][/tex]
Only these four combinations result in round and yellow seeds.
3. Count the number of times the "Round and Yellow" phenotype occurs out of the total combinations:
[tex]\[ \frac{\text{Number of "Round and Yellow" phenotypes}}{\text{Total number of combinations}} = \frac{4}{16} \][/tex]
Therefore, the ratio of offspring that will have round and yellow seeds is [tex]\( \frac{4}{16} \)[/tex], which simplifies to:
[tex]\[ 4:16 \][/tex]
Therefore, considering the given options, the ratio [tex]\( 4:16 \)[/tex] is indeed the correct answer. Among the provided options, this corresponds to [tex]\( \boxed{4:16} \)[/tex].
