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Prosecutor's fallacy

Hello there

I wonder if anyone might please be able to advise me?

I've been given the following question to answer on Prosecutor's fallacy:

Question 5 (10 marks): The “prosecutor’s fallacy” commonly crops up when considering DNA fingerprinting evidence. Consider the following scenario: DNA fingerprinting evidence from a crime scene in the UK indicates that 1 in 10,000 people will match the DNA profile found at the crime scene. For the purposes of this exercise assume that the frequencies of the alleles used do not deviate between different subpopulations of the UK, and that the crime was committed by someone from the UK. On DNA fingerprinting evidence alone what is the approximate probability that a suspect with a matching DNA profile is innocent of the crime? Explain your reasoning in 50 words or less.

I wonder if I have gone the correct way about calculating this ...

I first of all looked up the UK population. This earlier today was 65009664 (it changes every hour).
To find the number of suspects, I then did the calculation 65009664/10000 = 6500.9664
To find the number of innocent suspects, I then did: 6500.9664 - 1 = 6599.9664

Finally, I did the calculation
P (innocent|evidence) = 6499.9664/6500.9664 = 0.99984617671 or 99.98%

I'd be very appreciative if anyone could please steer me right.

Thank you :smile:

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