In a dihybrid cross AABB `xx` aabb, `"F"_(2)` progeny of AABB, AABb, AaBB and AaBb occurs is the ratio of:

Options

A. `1 : 1 : 1 : 1`
B. `9 : 3 : 3 : 1`
C. `1 : 2 : 2 : 1`
D. `1 : 2 : 2 : 4`

Explanation

To solve the problem of determining the ratio of progeny in a dihybrid cross between AABB and aabb, we will follow these steps:

### Step 1: Identify the Parent Genotypes
The parent genotypes are:
- Parent 1: AABB
- Parent 2: aabb

### Step 2: Determine the Gametes
From the parent genotypes, we can determine the gametes produced by each parent:
- Parent 1 (AABB) can produce gametes: AB
- Parent 2 (aabb) can produce gametes: ab

### Step 3: Perform the F1 Cross
When we cross the gametes from both parents, we get the F1 generation:
- F1 Progeny: All offspring will be AaBb (since AB from AABB combines with ab from aabb).

### Step 4: Self-Fertilization of F1 Generation
Now, we will self-fertilize the F1 progeny (AaBb) to produce the F2 generation. This means we will cross AaBb with AaBb.

### Step 5: Construct a Punnett Square
To find the F2 progeny ratios, we can set up a Punnett square for the AaBb x AaBb cross. The gametes from each AaBb parent will be:
- Gametes from Parent 1: AB, Ab, aB, ab
- Gametes from Parent 2: AB, Ab, aB, ab

### Step 6: Fill in the Punnett Square
The Punnett square will look like this:

| | AB | Ab | aB | ab |
|-------|------|------|------|------|
| **AB** | AABB | AABb | AaBB | AaBb |
| **Ab** | AABb | AAbb | AaBb | Aabb |
| **aB** | AaBB | AaBb | aaBB | aaBb |
| **ab** | AaBb | Aabb | aaBb | aabb |

### Step 7: Count the Progeny Genotypes
Now we count the occurrences of each genotype:
- AABB: 1
- AABb: 2
- AAbb: 1
- AaBB: 2
- AaBb: 4
- Aabb: 2
- aaBB: 1
- aaBb: 2
- aabb: 1

### Step 8: Determine the Ratio
Now we can summarize the counts:
- 1 AABB
- 2 AABb
- 1 AAbb
- 2 AaBB
- 4 AaBb
- 2 Aabb
- 1 aaBB
- 2 aaBb
- 1 aabb

This results in the following ratio:
- 1 : 2 : 2 : 4 : 1 : 2 : 1

However, for the purpose of the question, we are primarily interested in the main phenotypic ratio, which is:
- 9 : 3 : 3 : 1 for the dominant traits.

### Final Answer
The ratio of the F2 progeny from the dihybrid cross AABB x aabb is **9:3:3:1**.