Genetic Analysis of Pea Flower Color

To determine the probability of the third offspring having purple flowers, we must first identify the genotypes of the parent plants based on the given phenotypes and the resulting offspring.

1. Identification of Alleles and Genotypes

• Let \( P \) represent the dominant allele for purple flowers.
• Let \( p \) represent the recessive allele for white flowers.
• Since both parents have purple flowers but produced an offspring with white flowers (\( pp \)), each parent must carry one recessive allele.
• Therefore, both parents are heterozygous: \( Pp \times Pp \).

2. Determining the Probabilities

Using a Punnett square for the cross \( Pp \times Pp \), we can determine the expected genotypic and phenotypic ratios of the offspring:

𝑃 𝑝 𝑃 𝑃 𝑃 𝑃 𝑝 𝑝 𝑃 𝑝 𝑝 𝑝 P p ​ P PP Pp ​ p Pp pp ​ ​

The resulting phenotypes are:

• Purple flowers: \( PP \) or \( Pp \) (3 out of 4)
• White flowers: \( pp \) (1 out of 4)

The probability of an offspring having purple flowers is:

$$ P(\text{Purple}) = \frac{3}{4} = 0.75 $$

3. Calculation for the Third Offspring

In Mendelian genetics, each fertilization event is an independent event. The phenotype of previous offspring (such as the first offspring being white) does not influence the probability of the phenotype for subsequent offspring.

Thus, the probability that the third offspring will have purple flowers remains the same as any other individual offspring from this cross.

Probability: \( 0.75 \)

Final Answer:

The probability that the third offspring from these parents will have purple flowers is 0.75.