Problem Analysis: The question asks for the frequency of the allele 'p' in a given population. We are provided with the total population size and the counts for two genotypes: homozygous dominant (PP) and heterozygous (Pp). We need to derive the count for the homozygous recessive genotype (pp) to calculate the allele frequency.

Allele Frequency Calculation Steps

1. Determine the count of homozygous recessive (pp) individuals:

   • Total population size = Number of PP + Number of Pp + Number of pp
   • Given: Total = 10,000, PP = 2500, Pp = 3000
   • So, $10,000 = 2500 + 3000 + \text{Number of pp}$
   • Number of pp = $10,000 - 2500 - 3000 = 4500$

2. Calculate the total number of alleles in the population:

   • Each individual has 2 alleles.
   • Total alleles = Total population size $\times$ 2
   • Total alleles = $10,000 \times 2 = 20,000$

3. Calculate the total number of 'p' alleles:

   • The 'p' allele is present in both heterozygous (Pp) and homozygous recessive (pp) individuals.
   • Each 'Pp' individual contributes one 'p' allele.
   • Each 'pp' individual contributes two 'p' alleles.
   • Number of 'p' alleles = (Number of Pp $\times$ 1) + (Number of pp $\times$ 2)
   • Number of 'p' alleles = ($3000 \times 1$) + ($4500 \times 2$)
   • Number of 'p' alleles = $3000 + 9000 = 12,000$

4. Calculate the frequency of the 'p' allele:

   • Frequency of 'p' ($q$) = $\frac{\text{Total number of 'p' alleles}}{\text{Total number of alleles}}$
   • $q = \frac{12,000}{20,000}$
   • $q = \frac{12}{20} = \frac{3}{5} = 0.6$

Final Result

The frequency of allele p in the population is calculated to be 0.6.