In pea plants, purple color of flowers is determined by the dominant allele while white
color is determined by the recessive allele. A genetic cross between two purple flower-
bearing plants results in an offspring with white flowers. The probability that the third
offspring from these parents will have purple flowers is
(rounded off to 2 decimal
Official Answer Key:
0.75 to 0.75
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2019 Q.57)**
**1. Governing Concept & Definition**:
- **Topic**: Classical Mendelian Genetics & Monohybrid Cross
- Let $P$ be the dominant allele for purple flowers and $p$ be the recessive allele for white flowers.
- Heterozygous plant genotype: $Pp$
- Cross: $Pp \times Pp$.
**2. Detailed Step-by-Step Calculation**:
- **Genotypic Ratio**:
$1\text{ }PP : 2\text{ }Pp : 1\text{ }pp$
- **Phenotypes**:
- Purple flower phenotype ($PP$ and $Pp$): $\frac{1}{4} + \frac{2}{4} = \frac{3}{4} = 0.75$
- White flower phenotype ($pp$): $\frac{1}{4} = 0.25$
- The probability that a random progeny plant has purple flowers is $0.75$.
**3. Final Answer**:
- **Calculated Value**: **0.75**
- **Official GATE Accepted Range**: **0.75 to 0.75**
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