Step 1: Understanding the Question:
The question asks for the observable physical ratio (phenotypic ratio) of offspring resulting from a dihybrid cross in the second filial (F\(_2\)) generation.
Step 2: Key Formula or Approach:
A dihybrid cross studies two pairs of contrasting traits simultaneously.
The ratio is derived using the Law of Independent Assortment and a \(4 \times 4\) Punnett square.
Step 3: Detailed Explanation:
In Mendel's experiments (e.g., Round-Yellow \(RRYY\) \(\times\) Wrinkled-Green \(rryy\)), the F\(_1\) generation is heterozygous (\(RrYy\)).
When F\(_1\) plants are selfed, they produce four types of gametes: \(RY, Ry, rY, ry\).
The combination of these gametes results in \(16\) possible outcomes:
1. Dominant for both traits: \(9\) (Round Yellow)
2. Dominant for first, recessive for second: \(3\) (Round Green)
3. Recessive for first, dominant for second: \(3\) (Wrinkled Yellow)
4. Recessive for both traits: \(1\) (Wrinkled Green)
Step 4: Final Answer:
The resulting phenotypic ratio is \(9:3:3:1\).