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Home » Solution: The average of the five values is given by - Abbey Badges

Solution: The average of the five values is given by - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Dr. Elena models contamination risk: each DNA sample has a 2% chance of contamination during handling. If 50 samples are processed, what is the probability that exactly 2 are contaminated?

📌 This is a binomial probability: C(50,2) × (0.02)² × (0.98)⁴⁸.

📌 C(50,2) = (50×49)/2 = <<50*49/2=1225>>1225.

📌 So, 1225 × 0.0004 × 0.3642 ≈ <<1225*0.0004*0.3642=0.1785>>0.1785.

📌 #### 0.178

📌 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.

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