Dr. Elena assesses a mixed sample with two contributors. Each has an independent 8% chance of triggering a false match in a search. What is the probability that at least one contributor produces a false match in the same sample?

February 22, 2026

Dr. Elena assesses a mixed sample with two contributors. Each has an independent 8% chance of triggering a false match in a search. What is the probability that at least one contributor produces a false match in the same sample?

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Alex calculates that a suspect DNA profile matches a database entry in 1 out of every 1,000 people. In a city with 4.5 million people, how many matches are expected in the city database? If the police focus on a subnet of 15,000 individuals, how many matches would be expected?
City-wide expected matches: 4,500,000 × (1/1000) = <<4500000/1000=4500>>4,500.
Subset expected matches: (4500 / 4,500,000) × 15,000 = (0.001) × 15,000 = <<0.001*15000=15>>15.
Probability of no false match: 1 – 0.08 = 0.92.
Probability both pass: 0.92 × 0.92 = <<0.92*0.92=0.8464>>0.8464.
So, probability of at least one false match: 1 – 0.8464 = <<1-0.8464=0.1536>>0.1536.

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