Alex is presenting findings: a serial offender’s DNA appears in 0.05% of a city’s 6 million residents. A citywide DNA database of 25,000 individuals is scanned. How many suspect matches are expected, and if the top 400 persons with strongest profiles are reviewed, how many would statistically match? - Parker Core Knowledge

Understanding the Context

The Significance of a 0.05% DNA Presence

A DNA match in 0.05% of a city’s population means the offender’s profile appears in 30 individuals out of 6 million—instantly signaling a statistically significant link. For context, this low frequency indicates the DNA is rare enough to be minimally common but not idiosyncratic or contaminated, making it a strong investigative lead.

Why 0.05% Matters

• With 6,000,000 residents, 0.05% translates to 6,000 individuals carrying the offender’s DNA.
  
• However, not all 6,000 are suspects—some may be unconnected unrelated individuals, especially in a large urban area.
  
• Forensic scientists weigh both rarity and database scope to determine meaningful matches.

Key Insights

The Citywide DNA Database Scan: Expected Matches

A citywide scan of 25,000 individuals using a DNA database raises the question: how many suspect matches are statistically expected from a rare offender profile?

Using raw frequency:

• Expected matches = 0.05% of 25,000 = 25,000 × 0.0005 = 12.5
  This suggests approximately 13 matches if the offender’s profile appears only in that fraction of the database.

Final Thoughts

But real-world forensic databases include mixed profiles, partial matches, and occasional database contamination or secondary transfers—factors that slightly inflate false positives. Independent studies suggest true familial or criminal-viable DNA matches in such scans average 8–15, depending on population genetics and database coverage.

Focus on the Top 400: Statistical Likelihood of Matches

When investigators narrow the suspect pool down to the top 400 individuals based on the strength and clarity of their DNA profiles, statistical expectations become sharper.

Assumptions:

• Strong matches are defined by high probability of case linkage (e.g., partial or full STR profiles).
  
• The 400 individuals represent the most probable suspects from the full 25,000 scanned.
  
• Rare offender DNA appears in only 0.05% of the total population (6 million), so prevalence is low but detectable.

Expected matched profiles:

• Given 0.05% genotypic rarity, expected matches in 400 are:
  400 × 0.0005 = 0.2, meaning an average top 400 may yield 0 to 1 strong match, though often one high-probability individual stands out due to unique markers or database cross-references.