To determine the value of [tex]\( p \)[/tex], given that the allele for short legs (recessive) is represented by [tex]\( q \)[/tex] and 21 out of 100 organisms have short legs, we start with the information provided.
1. Determine [tex]\( q \)[/tex]:
Since 21 out of 100 organisms have short legs, this corresponds to the recessive phenotype. The frequency of the recessive allele ([tex]\( q \)[/tex]) can be represented as:
[tex]\[
q = \frac{21}{100} = 0.21
\][/tex]
2. Calculate [tex]\( p \)[/tex]:
We know that the sum of the frequencies of the dominant allele ([tex]\( p \)[/tex]) and the recessive allele ([tex]\( q \)[/tex]) must equal 1:
[tex]\[
p + q = 1
\][/tex]
Given [tex]\( q = 0.21 \)[/tex]:
[tex]\[
p = 1 - q = 1 - 0.21 = 0.79
\][/tex]
After determining [tex]\( p \)[/tex], we verify we have utilized the equation [tex]\( p + q = 1 \)[/tex]. Since [tex]\( p = 0.79 \)[/tex] and [tex]\( q = 0.21 \)[/tex], adding these values should yield:
[tex]\[
p + q = 0.79 + 0.21 = 1
\][/tex]
Therefore, the correct value of [tex]\( p \)[/tex] is [tex]\( 0.79 \)[/tex].
Thus, the answer is:
[tex]\[
\boxed{0.79}
\][/tex]
