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For 12 independent markers: 0.95¹² ≈ <<0.95^12=0.54036>>0.54036.
So, the probability is approximately 0.540.
#### 0.540
Alex calculates that a DNA match occurs in 0.2% of the population. In a city of 8 million, how many individuals would be expected to match, and if law enforcement screens 50,000 people, how many matches would they expect to find?
Expected matches in 8 million: 8,000,000 × 0.002 = <<8000000*0.002=16000>>16,000.
For 50,000 screened: (16,000 / 8,000,000) × 50,000 = (0.002) × 50,000 = <<0.002*50000=100>>100.
Dr. Elena is analyzing a partial DNA profile where each locus has a 10% chance of being successfully amplified. If 15 loci are tested independently, what is the probability that at least one locus is successfully amplified?
Probability of failure at one locus: 1 – 0.1 = 0.9.
Probability all 15 fail: 0.9¹⁵ ≈ <<0.9^15=0.20589>>0.20589.
