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The allele for long legs is dominant and is represented by [tex][tex]$p$[/tex][/tex]. The allele for short legs is recessive and is represented by [tex][tex]$q$[/tex][/tex]. The Hardy-Weinberg equation is shown below:
[tex]\[ p^2 + 2pq + q^2 = 1 \][/tex]
If 33 out of 100 organisms have short legs, what is [tex][tex]$p$[/tex][/tex]?
To find the value of [tex]\( p \)[/tex] given that 33 out of 100 organisms have short legs, we will follow these steps based on the Hardy-Weinberg equilibrium.
1. Understanding Hardy-Weinberg Equilibrium: The Hardy-Weinberg equation is [tex]\( p^2 + 2pq + q^2 = 1 \)[/tex]. Here: - [tex]\( p \)[/tex] represents the frequency of the dominant allele (legs). - [tex]\( q \)[/tex] represents the frequency of the recessive allele (short legs). - [tex]\( p^2 \)[/tex] is the proportion of the population that is homozygous dominant (having two dominant alleles). - [tex]\( 2pq \)[/tex] is the proportion of the population that is heterozygous (having one dominant and one recessive allele). - [tex]\( q^2 \)[/tex] is the proportion of the population that is homozygous recessive (having two recessive alleles).
2. Identifying the Given Information: - Total number of organisms, [tex]\( N \)[/tex], is 100. - Number of organisms with short legs, which corresponds to the homozygous recessive group ([tex]\( q^2 \)[/tex]), is 33.
3. Calculate [tex]\( q^2 \)[/tex]: [tex]\[
q^2 = \frac{\text{Number of homozygous recessive organisms}}{\text{Total number of organisms}} = \frac{33}{100} = 0.33
\][/tex]
4. Determine [tex]\( q \)[/tex] by taking the square root of [tex]\( q^2 \)[/tex]: [tex]\[
q = \sqrt{0.33} \approx 0.574
\][/tex]
5. Use the relationship [tex]\( p + q = 1 \)[/tex] to find [tex]\( p \)[/tex]: [tex]\[
p = 1 - q = 1 - 0.574 \approx 0.426
\][/tex]
6. Final Value of [tex]\( p \)[/tex]: [tex]\[
p \approx 0.426
\][/tex]
Therefore, the closest option to the calculated value of [tex]\( p \)[/tex] is option C: [tex]\[
\boxed{0.43}
\][/tex]
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