To answer this question, let's analyze the probability of each individual trait and then the probability of both traits occurring together.
### Step 1: Determine the Probability of Green Seeds
Green seeds are denoted by the genotype `yy`:
1. Each parent has a genotype of `Yy`.
2. When two `Yy` parents are crossed, the possible genotypes of the offspring are `YY`, `Yy`, `Yy`, and `yy`.
This yields the ratio:
- `YY` : 1
- `Yy` : 2
- `yy` : 1
So, the probability of getting `yy` (green seeds) is:
[tex]\[ \frac{1}{4} \][/tex]
### Step 2: Determine the Probability of Wrinkled Seeds
Wrinkled seeds are denoted by the genotype `rr`:
1. Each parent has a genotype of `Rr`.
2. When two `Rr` parents are crossed, the possible genotypes of the offspring are `RR`, `Rr`, `Rr`, and `rr`.
This yields the ratio:
- `RR` : 1
- `Rr` : 2
- `rr` : 1
So, the probability of getting `rr` (wrinkled seeds) is:
[tex]\[ \frac{1}{4} \][/tex]
### Step 3: Combine the Probabilities for Both Traits
Since the traits for seed color and seed shape are inherited independently (according to Mendel's law of independent assortment), we can multiply the individual probabilities to find the probability of both traits occurring together.
[tex]\[ \text{Probability of } \text{yy} \, (\text{green}) = \frac{1}{4} \][/tex]
[tex]\[ \text{Probability of } \text{rr} \, (\text{wrinkled}) = \frac{1}{4} \][/tex]
Thus, the combined probability of having green and wrinkled seeds (`yy` and `rr`) is:
[tex]\[ \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \][/tex]
Therefore, the probability of having green and wrinkled seeds in this dihybrid cross is:
[tex]\[ \frac{1}{16} \][/tex]
This corresponds to the answer choice:
[tex]\( 1 : 16 \)[/tex]
