To solve the problem of determining the percentage of progenies with broad leaves and pink flowers in the F2 generation of snapdragons, we need to analyze the traits involved and their inheritance patterns.
### Step-by-Step Solution:
1. **Identify the Traits and Their Inheritance Patterns:**
- The first trait (broad leaves) follows the law of dominance, where the dominant allele (B) results in broad leaves, while the recessive allele (b) results in narrow leaves.
- The second trait (flower color) shows incomplete dominance, where the homozygous red (RR) produces red flowers, the homozygous white (rr) produces white flowers, and the heterozygous (Rr) produces pink flowers.
2. **Determine the Genotypes for the F1 Generation:**
- When we cross a homozygous broad-leaved plant (BB) with a homozygous narrow-leaved plant (bb), all F1 progeny will be heterozygous (Bb) and will exhibit broad leaves due to the dominance of B over b.
- For the flower color, if we cross a homozygous red flower plant (RR) with a homozygous white flower plant (rr), all F1 progeny will be heterozygous (Rr) and will exhibit pink flowers due to incomplete dominance.
3. **Cross the F1 Generation to Get the F2 Generation:**
- The F1 generation plants are BbRr (broad leaves and pink flowers).
- To find the F2 generation, we perform a dihybrid cross of BbRr x BbRr.
4. **Set Up a Punnett Square:**
- For the traits, we can create a Punnett square for the two traits:
- Gametes from each parent:
- Bb can produce B or b
- Rr can produce R or r
- This results in the following combinations:
- BR, Br, bR, br
5. **Calculate the F2 Generation Ratios:**
- The resulting combinations from the Punnett square will be:
- BBRR (broad, red)
- BBRr (broad, pink)
- BbRR (broad, red)
- BbRr (broad, pink)
- bbRR (narrow, red)
- bbRr (narrow, pink)
- BbrR (broad, pink)
- BbrR (broad, pink)
- bbrr (narrow, white)
- The total combinations will give us 16 possible outcomes.
6. **Count the Desired Phenotype:**
- We are interested in the phenotype with broad leaves and pink flowers (BbRr).
- From the combinations, we find that there are 6 instances of broad leaves and pink flowers.
7. **Calculate the Percentage:**
- The percentage of progenies with broad leaves and pink flowers in the F2 generation is:
\[
\text{Percentage} = \left( \frac{\text{Number of broad leaves and pink flowers}}{\text{Total number of progenies}} \right) \times 100
\]
\[
\text{Percentage} = \left( \frac{6}{16} \right) \times 100 = 37.5\%
\]
### Final Answer:
The percentage of progenies with broad leaves and pink flowers in the F2 generation of snapdragons is **37.5%**.
