If a plant with genotype AaBb is self-fertilized , the probability of getting AABB genotype will be ( A and B are not linked )

Options

A. `1//2`
B. `1//4`
C. `1//3`
D. `1//16`

Answer

To solve the problem of finding the probability of obtaining the genotype AABB from a self-fertilization of a plant with the genotype AaBb, we can follow these steps:

### Step 1: Understand the Genotype
The plant has the genotype AaBb, which means it is heterozygous for both traits A and B.

### Step 2: Set Up the Punnett Square
Since both traits are independent (not linked), we can use a Punnett square to find the possible genotypes from the self-fertilization of AaBb x AaBb.

### Step 3: Determine Gametes
The possible gametes from each parent (AaBb) are:
- AB
- Ab
- aB
- ab

### Step 4: Create the Punnett Square
We will create a 4x4 Punnett square using the gametes from both parents:

| | 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 5: Count the Genotypes
From the Punnett square, we can 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 6: Calculate Total Outcomes
The total number of outcomes (or zygotes) is 16 (4 from each row and 4 from each column).

### Step 7: Calculate Probability
The probability of getting the genotype AABB is the number of AABB genotypes divided by the total number of genotypes:
\[ \text{Probability of AABB} = \frac{\text{Number of AABB}}{\text{Total Genotypes}} = \frac{1}{16} \]

### Final Answer
The probability of obtaining the genotype AABB from the self-fertilization of a plant with genotype AaBb is \( \frac{1}{16} \).

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