What proportion of individuals will have the genotype PpQQRrSstt if their parents had genotypes PPQqRRssTt and PpQQrrSSTt ?

Options

A. `1//8`
B. `1//16`
C. `1//256`
D. `1//64`

Answer

To solve the problem of determining the proportion of individuals with the genotype PpQQRrSstt from the given parental genotypes PPQqRRssTt and PpQQrrSSTt, we will follow these steps:

### Step 1: Analyze the Genotype for Each Gene
We will analyze each gene (P, Q, R, S, and T) separately.

#### Gene P:
- Parent 1: PP (homozygous dominant)
- Parent 2: Pp (heterozygous)

Possible offspring genotypes:
- From PP x Pp, the offspring can be:
- PP (from P and P)
- Pp (from P and p)

So, the possible genotypes are:
- PP: 1
- Pp: 1

Total: 2 (1 PP + 1 Pp)

Proportion of Pp = 1/2

### Step 2: Analyze Gene Q
- Parent 1: QQ (homozygous dominant)
- Parent 2: QQ (homozygous dominant)

Possible offspring genotypes:
- From QQ x QQ, the offspring can only be:
- QQ

So, the possible genotypes are:
- QQ: 2

Total: 2 (2 QQ)

Proportion of Q = 2/2 = 1

### Step 3: Analyze Gene R
- Parent 1: RR (homozygous dominant)
- Parent 2: rr (homozygous recessive)

Possible offspring genotypes:
- From RR x rr, the offspring can be:
- Rr (from R and r)

So, the possible genotypes are:
- Rr: 2

Total: 2 (2 Rr)

Proportion of R = 2/2 = 1

### Step 4: Analyze Gene S
- Parent 1: ss (homozygous recessive)
- Parent 2: SS (homozygous dominant)

Possible offspring genotypes:
- From ss x SS, the offspring can be:
- Ss (from S and s)

So, the possible genotypes are:
- Ss: 2

Total: 2 (2 Ss)

Proportion of S = 2/2 = 1

### Step 5: Analyze Gene T
- Parent 1: Tt (heterozygous)
- Parent 2: Tt (heterozygous)

Possible offspring genotypes:
- From Tt x Tt, the offspring can be:
- TT, Tt, Tt, tt

So, the possible genotypes are:
- TT: 1
- Tt: 2
- tt: 1

Total: 4 (1 TT + 2 Tt + 1 tt)

Proportion of tt = 1/4

### Step 6: Calculate the Overall Proportion
Now, we will multiply the proportions of each gene to find the overall proportion of the genotype PpQQRrSstt.

\[ \text{Overall Proportion} = \left(\frac{1}{2}\right) \times (1) \times (1) \times (1) \times \left(\frac{1}{4}\right) \]

Calculating this gives:
\[ \text{Overall Proportion} = \frac{1}{2} \times 1 \times 1 \times 1 \times \frac{1}{4} = \frac{1}{8} \]

### Final Answer
The proportion of individuals with the genotype PpQQRrSstt is **1/8**.

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