A Blooming Discovery: The Colorful World of Tulips!

What can we learn from a random sample of 1000 tulips in a cultivated field that yields 847 purple flowers and 153 pink flowers? a. Determine the frequency of the purple and pink alleles in this field population. b. Estimate the proportion of all purple flowering plants that are heterozygotes and homozygotes.

Oh, what a delightful sight it must be to wander through a field of vibrant tulips, each petal bursting with color and life! In this jolly adventure, let's explore the genetics behind these beautiful blooms.

A. Frequency of Purple and Pink Alleles

From our random sample of 1000 tulips, we found 847 purple flowers and 153 pink flowers. To determine the frequency of the purple and pink alleles, we can use the Hardy-Weinberg equilibrium formula:

p + q = 1

where:

p = frequency of dominant allele (purple)

q = frequency of recessive allele (pink)

Given that the frequency of pink flowers (cc) is 0.153:

Frequency of pink allele c (q) = √0.153 = 0.391

Therefore, frequency of purple allele C (p) = 1 - 0.391 = 0.609

So, in this enchanting field population, the purple allele (C) thrives at 0.609 frequency, while the pink allele (c) dances at 0.391 frequency!

B. Proportion of Purple Flowering Plants

Now, let’s estimate the proportion of all purple flowering plants that are heterozygotes and homozygotes:

Purple homozygotes (CC) = p² * total population = 0.609² * 1000 = 371

Purple heterozygotes (Cc) = 2pq * total population = 2 * 0.609 * 0.391 * 1000 = 476

With such a cheery mix of genetic combinations, these tulips bloom in various shades of purple, each one a unique masterpiece in this colorful field!

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