10. Random DNA hexamers containing A, T, G and C are generated by DNA synthesis. The fraction of the
hexamers that will have 3 purines followed by 3 pyrimidines is:
1. 9/46
2. 1/26
3. 6/46
4. 6C3/36

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Calculating the Probability of DNA Hexamers with Specific Purine-Pyrimidine Patterns

When randomly synthesizing DNA hexamers (sequences of 6 nucleotides), we can calculate the fraction of sequences with specific patterns based on nucleotide types: purines and pyrimidines.

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What are Purines and Pyrimidines?

• Purines: Adenine (A), Guanine (G)

• Pyrimidines: Cytosine (C), Thymine (T)

So, out of the 4 bases (A, T, G, C):

• 2 are purines → A, G

• 2 are pyrimidines → C, T

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The Problem:

You are asked to calculate the fraction of all possible random DNA hexamers that have:

3 purines followed by 3 pyrimidines

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Step-by-Step Calculation:

1. Total number of possible hexamers:
   Each of the 6 positions can be filled by A, T, G, or C →

46=4096 total possible hexamers4^6 = 4096 \text{ total possible hexamers}46=4096 total possible hexamers

2. Number of favorable hexamers (3 purines followed by 3 pyrimidines):

   • First 3 positions must be purines (A or G):
     For each position: 2 choices
     → $2\times 2\times 2=8$ combinations

   • Last 3 positions must be pyrimidines (C or T):
     For each position: 2 choices
     → $2\times 2\times 2=8$ combinations

   • Total favorable sequences:

     $$8\times 8=64$$

3. Fraction of favorable hexamers:

   644096=164\frac{64}{4096} = \frac{1}{64}409664=641

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✅ Correct Answer:

(2) 1/64

(Note: There’s likely a typographical error in the original options. The correct fraction is 1/64, not 1/26 or 9/46, etc.)

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Conclusion:

This problem shows how combinatorics and basic nucleotide classification help in computing specific DNA sequence probabilities. Such calculations are common in bioinformatics, genetic algorithm design, and synthetic biology. The key is breaking the problem into manageable segments and applying probability rules accordingly.