To determine the correct expression for the dominant allele [tex]\( k \)[/tex] in the given frog population, let's analyze the information step by step.
1. Identify the number of heterozygous dominant frogs:
- The number of heterozygous dominant frogs given is 34.
2. Identify the number of frogs with the recessive trait:
- The number of frogs with the recessive trait given is 16.
3. Calculate the total population of the frogs:
- Total population [tex]\(= \text{number of heterozygous dominant frogs} + \text{number of frogs with recessive trait}\)[/tex]
- [tex]\( \text{Total population} = 34 + 16 = 50 \)[/tex]
4. Determine the fraction of the dominant allele (k):
- The problem asks for the population with the dominant allele. The proportion given in the problem corresponds to the fraction relative to the total. Hence, using the total population (50) out of a maximum count (200):
- [tex]\( k_dominant_allele = \frac{\text{total population}}{200} = \frac{50}{200} \)[/tex]
So, the correct expression for [tex]\( k \)[/tex] dominant allele is:
C. [tex]\(\frac{50}{200}\)[/tex]
