Answer :
When crossing two plants that both have the genotype [tex]\( RrYy \)[/tex], we need to determine the probability of the offspring having round and yellow seeds. Let's break this down step by step:
### Step 1: Determine the possible gametes
Each [tex]\( RrYy \)[/tex] plant can produce four types of gametes due to the independent assortment of the genes [tex]\( R/r \)[/tex] and [tex]\( Y/y \)[/tex]:
- [tex]\( RY \)[/tex]
- [tex]\( Ry \)[/tex]
- [tex]\( rY \)[/tex]
- [tex]\( ry \)[/tex]
### Step 2: Construct a Punnett square
By creating a 4x4 Punnett square, we can list all possible combinations of these gametes.
[tex]\[ \begin{array}{c|c|c|c|c} & RY & Ry & rY & ry \\ \hline RY & \text{RRYY} & \text{RRYy} & \text{RrYY} & \text{RrYy} \\ \hline Ry & \text{RRYy} & \text{RRyy} & \text{RrYy} & \text{Rryy} \\ \hline rY & \text{RrYY} & \text{RrYy} & \text{rrYY} & \text{rrYy} \\ \hline ry & \text{RrYy} & \text{Rryy} & \text{rrYy} & \text{rryy} \\ \end{array} \][/tex]
### Step 3: Identify the genotypes that result in round and yellow seeds
The seed will be round if it has at least one [tex]\( R \)[/tex] allele (i.e., [tex]\( RR \)[/tex] or [tex]\( Rr \)[/tex]) and it will be yellow if it has at least one [tex]\( Y \)[/tex] allele (i.e., [tex]\( YY \)[/tex] or [tex]\( Yy \)[/tex]). Thus, the genotypes that produce round and yellow seeds are:
- [tex]\( RRYY \)[/tex]
- [tex]\( RRYy \)[/tex]
- [tex]\( RrYY \)[/tex]
- [tex]\( RrYy \)[/tex]
### Step 4: Count the desired genotypes in the Punnett square
Let's count how many times each of these desired genotypes appear in the Punnett square:
- [tex]\( RRYY \)[/tex]: 1
- [tex]\( RRYy \)[/tex]: 2
- [tex]\( RrYY \)[/tex]: 2
- [tex]\( RrYy \)[/tex]: 4
Adding these together, we get [tex]\( 1 + 2 + 2 + 4 = 9 \)[/tex].
### Step 5: Calculate the ratio
The total number of genotypes in the Punnett square is 16.
Thus, the ratio of offspring that will have round and yellow seeds is [tex]\( \frac{9}{16} \)[/tex].
### Conclusion
The ratio of offspring with round and yellow seeds is [tex]\( \frac{9}{16} \)[/tex], which corresponds to the option [tex]\( 9:16 \)[/tex].
### Step 1: Determine the possible gametes
Each [tex]\( RrYy \)[/tex] plant can produce four types of gametes due to the independent assortment of the genes [tex]\( R/r \)[/tex] and [tex]\( Y/y \)[/tex]:
- [tex]\( RY \)[/tex]
- [tex]\( Ry \)[/tex]
- [tex]\( rY \)[/tex]
- [tex]\( ry \)[/tex]
### Step 2: Construct a Punnett square
By creating a 4x4 Punnett square, we can list all possible combinations of these gametes.
[tex]\[ \begin{array}{c|c|c|c|c} & RY & Ry & rY & ry \\ \hline RY & \text{RRYY} & \text{RRYy} & \text{RrYY} & \text{RrYy} \\ \hline Ry & \text{RRYy} & \text{RRyy} & \text{RrYy} & \text{Rryy} \\ \hline rY & \text{RrYY} & \text{RrYy} & \text{rrYY} & \text{rrYy} \\ \hline ry & \text{RrYy} & \text{Rryy} & \text{rrYy} & \text{rryy} \\ \end{array} \][/tex]
### Step 3: Identify the genotypes that result in round and yellow seeds
The seed will be round if it has at least one [tex]\( R \)[/tex] allele (i.e., [tex]\( RR \)[/tex] or [tex]\( Rr \)[/tex]) and it will be yellow if it has at least one [tex]\( Y \)[/tex] allele (i.e., [tex]\( YY \)[/tex] or [tex]\( Yy \)[/tex]). Thus, the genotypes that produce round and yellow seeds are:
- [tex]\( RRYY \)[/tex]
- [tex]\( RRYy \)[/tex]
- [tex]\( RrYY \)[/tex]
- [tex]\( RrYy \)[/tex]
### Step 4: Count the desired genotypes in the Punnett square
Let's count how many times each of these desired genotypes appear in the Punnett square:
- [tex]\( RRYY \)[/tex]: 1
- [tex]\( RRYy \)[/tex]: 2
- [tex]\( RrYY \)[/tex]: 2
- [tex]\( RrYy \)[/tex]: 4
Adding these together, we get [tex]\( 1 + 2 + 2 + 4 = 9 \)[/tex].
### Step 5: Calculate the ratio
The total number of genotypes in the Punnett square is 16.
Thus, the ratio of offspring that will have round and yellow seeds is [tex]\( \frac{9}{16} \)[/tex].
### Conclusion
The ratio of offspring with round and yellow seeds is [tex]\( \frac{9}{16} \)[/tex], which corresponds to the option [tex]\( 9:16 \)[/tex].
