In a plant, smooth seeds (S) are dominant over wrinkled seeds(s) and green seeds (G) are dominant over yellow seeds (g). A plant homozygous for smooth and green seed is crossed with a plant having wrinkled and yellow seeds. The `F_(1)` offspring are self crossed to produce `F_(2)` generation. If a total of 160 offspring are produced, how many plants are expected to be having wrinkled and green seeds in `F_(2)` generation, according to a typical mendelian cross?

Options

A. 90
B. 30
C. 20
D. 10

Answer

To solve the problem step by step, we will follow the principles of Mendelian genetics.

### Step 1: Identify the Genotypes of the Parent Plants
- The first plant is homozygous for smooth and green seeds, which means its genotype is **SSGG** (Smooth seeds: S, Green seeds: G).
- The second plant is homozygous for wrinkled and yellow seeds, which means its genotype is **ssgg** (Wrinkled seeds: s, Yellow seeds: g).

### Step 2: Determine the Genotype of the F1 Generation
When we cross these two plants, the F1 generation will inherit one allele from each parent:
- From **SSGG** (Smooth and Green), we get **S** and **G**.
- From **ssgg** (Wrinkled and Yellow), we get **s** and **g**.

Thus, the genotype of all F1 offspring will be **SsGg** (Smooth and Green).

### Step 3: Self-Cross the F1 Generation to Produce F2 Generation
Now, we will self-cross the F1 generation (SsGg x SsGg). We can set up a Punnett square to determine the possible genotypes of the F2 generation.

### Step 4: Create a Punnett Square
The gametes from each parent (F1) will be:
- From the first parent: SG, Sg, sG, sg
- From the second parent: SG, Sg, sG, sg

The Punnett square will look like this:

| | SG | Sg | sG | sg |
|-------|------|------|------|------|
| **SG** | SS GG | SS Gg | Ss GG | Ss Gg |
| **Sg** | SS Gg | SS gg | Ss Gg | Ss gg |
| **sG** | Ss GG | Ss Gg | ss GG | ss Gg |
| **sg** | Ss Gg | Ss gg | ss Gg | ss gg |

### Step 5: Count the Genotypes
Now, we can count the genotypes that result from the Punnett square:
- **SSGG**: 1
- **SSGg**: 2
- **SsGG**: 2
- **SsGg**: 4
- **SSgg**: 1
- **Ssgg**: 2
- **ssGG**: 1
- **ssGg**: 2
- **ssgg**: 1

### Step 6: Identify the Desired Phenotype
We are looking for plants that have **wrinkled (ss)** and **green (G)** seeds. The possible genotypes that fit this description are:
- **ssGG** (Wrinkled and Green)
- **ssGg** (Wrinkled and Green)

From the counts:
- **ssGG**: 1
- **ssGg**: 2

Total for wrinkled and green seeds in F2 = 1 + 2 = 3.

### Step 7: Calculate the Total Offspring
The total number of offspring in the F2 generation is 16 (from the Punnett square).

### Step 8: Calculate the Expected Number of Wrinkled and Green Seeds in 160 Offspring
To find the expected number of plants with wrinkled and green seeds in a total of 160 offspring:
- The fraction of wrinkled and green seeds = 3 out of 16.
- Expected number = (3/16) * 160 = 30.

### Final Answer
Thus, the expected number of plants having wrinkled and green seeds in the F2 generation is **30**.

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