Carrier frequency among unaffected/normal individuals in population genetics:

• Given recessive allele frequency $q = 0.50$, dominant allele frequency $p = 1 - q = 0.50$.
• In genetic counseling and population genetics, when referring to a recessive genetic disorder, 'frequency of carriers' is evaluated among the phenotypically normal (non-affected) segment of the population, because affected individuals ($aa$) display the disease phenotype and are not merely healthy 'carriers':
  $\text{Carrier frequency among phenotypically normal} = \frac{2pq}{p^2 + 2pq} = \frac{2q}{1 + q}$.
• Calculation:
  $\frac{2 \times 0.50}{1 + 0.50} = \frac{1.00}{1.50} = \frac{2}{3} \approx 0.667 \approx 0.67$.
  
  Option analysis:
  Option 1 ($0.67$) is the exact proportion of carriers among phenotypically normal individuals (Key 1).

Historical facts regarding Hardy-Weinberg equilibrium:

• Wilhelm Weinberg ($1862\text{--}1937$) was a German physician and obstetrician practicing in Stuttgart, Germany (G.H. Hardy was the English mathematician). Statement (I) incorrectly states that Weinberg was an English mathematician.
• The Hardy-Weinberg principle was formulated independently by G.H. Hardy and Wilhelm Weinberg in $1908$, NOT $1938$. Statement (II) is incorrect.
  
  Option analysis:
  Both Statement (I) and Statement (II) are historically incorrect. Hence, Option 2 is the correct answer (Key 2).

Population genetics principles (Migration and Inbreeding):

• Effect of immigration on allele frequency:
  $\Delta q = m(q_m - q)$, where $m$ is the immigration rate, $q_m$ is the allele frequency in immigrants, and $q$ is the frequency in natives. Thus, $\Delta q$ depends directly on $m$ and $(q_m - q)$. Statement (I) is correct.
• Effect of inbreeding on total genetic variance:
  Inbreeding increases homozygosity and disperses allele frequencies between lines. For an additive trait, the total genetic variance among all individuals in an inbred population becomes $V_G = (1 + F)V_A$, where $F$ is Wright's inbreeding coefficient. As $F$ increases, the total additive genetic variance increases. Statement (II) is correct.
  
  Option analysis:
  Both Statement (I) and Statement (II) are correct, making Option 1 the correct answer (Key 1).