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In a species of flowers, homozygotes for the CR allele are red, homozygotes for the CW allele are
white, and heterozygotes are pink. If the
frequency of the CR allele is 0.8, what percentage of
the population is pink? Assume the population
is in Hardy-Weinberg equilibrium.



Answer :

GinnyAnswer
Sure! To determine the percentage of the population that is pink, we'll rely on the principles of Hardy-Weinberg equilibrium. Let's walk through the steps together:

1. Determine the frequency of the [tex]\( CW \)[/tex] allele:

Let [tex]\( p \)[/tex] represent the frequency of the [tex]\( CR \)[/tex] allele and [tex]\( q \)[/tex] represent the frequency of the [tex]\( CW \)[/tex] allele.

Given:
- [tex]\( p = 0.8 \)[/tex]

Since the total allele frequency in the population must sum to 1:
[tex]\[ p + q = 1 \][/tex]
Therefore:
[tex]\[ q = 1 - p \][/tex]
Substituting the value of [tex]\( p \)[/tex]:
[tex]\[ q = 1 - 0.8 = 0.2 \][/tex]

2. Calculate the frequency of heterozygotes (CRCW):

According to Hardy-Weinberg equilibrium, the frequency of heterozygotes (CRCW) in the population is given by:
[tex]\[ 2pq \][/tex]
Substituting the values of [tex]\( p \)[/tex] and [tex]\( q \)[/tex]:
[tex]\[ 2pq = 2 \times 0.8 \times 0.2 = 2 \times 0.16 = 0.32 \][/tex]

3. Convert the frequency to a percentage:

To find the percentage of the population that is pink, multiply the frequency by 100:
[tex]\[ \text{Percentage of pink flowers} = 0.32 \times 100 = 32\% \][/tex]

### Summary
The percentage of the population that is pink is [tex]\( \boxed{32\%} \)[/tex].

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