In Garden Pea, yellow colour of cotyledons is dominant over green and round shape of seed is dominant over wrinkled. When a plant with yellow and round seeds is crossed with a plant having yellow and wrinkled seeds, the progeny showed segregation for all the four characters. The probability of obatining green round seeds in the progeny of this case is

Options

A. `1//8`
B. `1//16`
C. `1//4`
D. `3//16`

Answer

To solve the problem, we need to analyze the genetic cross between two plants with different seed characteristics. Here’s a step-by-step solution:

### Step 1: Identify the Traits and Their Dominance
In Garden Pea:
- Yellow cotyledons (Y) are dominant over green cotyledons (y).
- Round seeds (R) are dominant over wrinkled seeds (r).

### Step 2: Determine the Genotypes of the Parents
We have two parents:
1. **Parent 1**: Yellow and round seeds (homozygous dominant for yellow and heterozygous for round) = Genotype: YYRR
2. **Parent 2**: Yellow and wrinkled seeds (homozygous dominant for yellow and homozygous recessive for wrinkled) = Genotype: YYrr

### Step 3: Determine the Gametes Produced by Each Parent
- **Parent 1 (YYRR)** can produce gametes: YR
- **Parent 2 (YYrr)** can produce gametes: Yr

### Step 4: Perform the Cross
Now we will cross the gametes:
- Gametes from Parent 1: YR
- Gametes from Parent 2: Yr

The possible combinations from the cross are:
- YR x Yr = YYRr (Yellow and Round)
- YR x Yr = YYrr (Yellow and Wrinkled)

### Step 5: Analyze the Progeny
From the cross, the phenotypes of the progeny are:
- YYRr: Yellow and Round
- YYrr: Yellow and Wrinkled

Since both parents are yellow, we will not see any green seeds in this generation.

### Step 6: Consider the Next Generation
To obtain green round seeds, we need to consider a cross that includes the recessive traits. To do this, we need to cross the progeny of the first generation (YYRr and YYrr) with a plant that has green seeds (yy).

### Step 7: Calculate the Probability of Green Round Seeds
To find the probability of obtaining green round seeds (yyR_), we need to consider the genotypes:
- The only way to get green seeds is if we have a recessive allele (yy).
- For round seeds, we need at least one dominant allele (R).

If we cross a yellow round (YYRr) with a green round (yyRr), the gametes will be:
- From yellow round: YR, Yr, YR, Yr
- From green round: yR, yr

The possible combinations will yield:
- YYRr (Yellow Round)
- YYrr (Yellow Wrinkled)
- YyRr (Yellow Round)
- Yyrr (Yellow Wrinkled)
- yyRr (Green Round)
- yyrr (Green Wrinkled)

### Step 8: Count the Phenotypes
From the combinations, we can see that:
- Yellow Round: 4
- Yellow Wrinkled: 2
- Green Round: 1
- Green Wrinkled: 1

### Step 9: Calculate the Probability
The total number of phenotypes is 8. The probability of obtaining green round seeds (yyR_) is:
- Probability = Number of Green Round Seeds / Total Progeny = 1 / 8

### Final Answer
The probability of obtaining green round seeds in the progeny is **1/8**.

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