A plant with genotype AABCcDD is self polinated. Provided that the four genes are independently assorting, what proportion of the progeny will show the genotype AAbbccDD?

Options

A. `1/4`
B. `1/16`
C. `1/64`
D. `1/256`

Answer

To solve the problem of determining the proportion of progeny with the genotype AAbbccDD from a self-pollination of a plant with the genotype AABCcDD, we can follow these steps:

### Step 1: Identify the Gametes
The parent plant has the genotype AABCcDD. We need to determine the gametes produced by this plant.

- For **A**: The plant is homozygous (AA), so it can only produce gametes with **A**.
- For **B**: The plant is heterozygous (Bb), so it can produce gametes with either **B** or **b**.
- For **C**: The plant is heterozygous (Cc), so it can produce gametes with either **C** or **c**.
- For **D**: The plant is homozygous (DD), so it can only produce gametes with **D**.

Thus, the possible gametes from this plant are:
- A B C D
- A B c D
- A b C D
- A b c D

### Step 2: Count the Total Gametes
From the above analysis, we can see that the total number of different gametes produced by the plant is 4:
1. A B C D
2. A B c D
3. A b C D
4. A b c D

### Step 3: Construct the Punnett Square
To find the genotypes of the progeny, we can use a Punnett square. Since we have 4 types of gametes from the self-pollination, we will create a 4x4 Punnett square.

### Step 4: Fill in the Punnett Square
We will fill in the Punnett square with the combinations of the gametes:

| | 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: Identify the Desired Genotype
We are looking for the genotype AAbbccDD. From the Punnett square, we can see that:
- The only combination that results in AAbb is from the gametes AABb and AAbb.

### Step 6: Calculate the Proportion
Now, we need to count how many of the progeny have the genotype AAbb:
- There are 1 AABB and 3 AABb which do not match our desired genotype.
- The only progeny that matches AAbb is 1.

Since we have a total of 16 possible combinations (4 gametes x 4 gametes), the proportion of progeny with the genotype AAbbccDD is:
\[ \text{Proportion} = \frac{1}{16} \]

### Final Answer
The proportion of progeny that will show the genotype AAbbccDD is **1/16**.

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