What is the probability of getting a progeny with AABbCcdd from selfing of tetrahybrid parent ?

Options

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

Answer

To solve the problem of finding the probability of obtaining a progeny with the genotype AABbCcdd from the selfing of a tetrahybrid parent (AaBbCcDd), we will follow a systematic approach:

### Step 1: Identify the Genotype of the Parents
The tetrahybrid parent has the genotype AaBbCcDd. Since we are selfing this parent, the second parent will also have the same genotype: AaBbCcDd.

### Step 2: Determine the Probability for Each Trait
We will analyze each trait (gene) separately to find the probability of obtaining the desired alleles.

#### Trait 1: A (AABbCcdd)
- We need to find the probability of getting AA from Aa x Aa.
- Possible offspring genotypes: AA, Aa, Aa, aa.
- Probability of AA = 1 (AA) out of 4 total = 1/4.

#### Trait 2: B (AABbCcdd)
- We need to find the probability of getting Bb from Bb x Bb.
- Possible offspring genotypes: BB, Bb, Bb, bb.
- Probability of Bb = 2 (Bb) out of 4 total = 2/4 = 1/2.

#### Trait 3: C (AABbCcdd)
- We need to find the probability of getting Cc from Cc x Cc.
- Possible offspring genotypes: CC, Cc, Cc, cc.
- Probability of Cc = 2 (Cc) out of 4 total = 2/4 = 1/2.

#### Trait 4: D (AABbCcdd)
- We need to find the probability of getting dd from Dd x Dd.
- Possible offspring genotypes: DD, Dd, Dd, dd.
- Probability of dd = 1 (dd) out of 4 total = 1/4.

### Step 3: Calculate the Overall Probability
To find the overall probability of obtaining the genotype AABbCcdd, we multiply the probabilities of each trait together:

\[ \text{Total Probability} = P(A) \times P(B) \times P(C) \times P(D) \]
\[ = \left(\frac{1}{4}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{4}\right) \]
\[ = \frac{1 \times 1 \times 1 \times 1}{4 \times 2 \times 2 \times 4} = \frac{1}{64} \]

### Final Answer
The probability of getting a progeny with genotype AABbCcdd from selfing a tetrahybrid parent is **1/64**.

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