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Question

In DNA fingerprinting, the use of multiple, highly polymorphic loci is crucial for accurate identification.  If a single locus has a probability of 0.1 of matching randomly between two unrelated individuals, what is the approximate probability of a match at 5 independent loci?

NISHANTH · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
 **Primary Concept**: Probability of independent events
 **Related Topics**: DNA fingerprinting, statistical independence
 **Prerequisites**: Understanding of probability multiplication for independent events.
## SOLUTION PATHWAY
**Given Information**:
  Probability of a match at a single locus, $P(match\_single) = 0.1$
  Number of independent loci, $n = 5$
  The loci are independent, meaning a match at one locus does not affect the probability of a match at another.
**Method & Steps**:
 1. Calculate the probability of a match at all 5 loci.
  Reasoning: Since the loci are independent, the probability of a match at all 5 loci is the product of the probabilities of a match at each individual locus.
  Formula/Rule: $P(match\_all) = P(match\_single)^n$
 2. Substitute the given values into the formula.
  Working: $P(match\_all) = (0.1)^5 = 0.00001$
  Key Point:  The probability decreases significantly as the number of loci increases. This is the basis for the high accuracy of DNA fingerprinting.
 3. State the final result.
  Result: The probability of a match at all 5 loci is 0.00001.
  Verification: The calculation is straightforward and easily verifiable.
 ## OPTION ANALYSIS
A ✓: 0.00001 is the correct probability calculated from the multiplication of independent probabilities. 
B :x: 0.0001 is an incorrect calculation; it likely represents a misunderstanding of how probabilities of independent events are combined.
C :x: 0.001 is also incorrect; it represents a smaller exponent in the calculation.
D :x: 0.1 represents the probability for a single locus only and fails to account for the multiple loci. 
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Adding probabilities instead of multiplying them: Independent probabilities are multiplied, not added. To avoid this, remember that the probability of multiple independent events occurring is always less than the probability of any single event.
  2. Incorrect exponent: Ensure the exponent is the number of loci being considered.
 **Quick Tips**:
  1. For independent events, use the formula $P(A \cap B) = P(A) * P(B)$ for two events, and generalize to $P(A_1 \cap A_2 \cap ... \cap A_n) = P(A_1) * P(A_2) * ... * P(A_n)$ for n events.
  2. Remember that the more loci used in DNA fingerprinting, the lower the chance of a random match.

NISHANTH · Answer

The correct Option is "0.00001"

NISHANTH · Answer

0.0001

NISHANTH · Answer

0.001

NISHANTH · Answer

0.1

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