CharlesBerger

The actual exercise comes after the slides below (skip them if you like).

The wish is father to the thought...

• Prosecutor’s fallacy (transposed conditional)
• Defense fallacy

• Verdict of the Court:

“According to the examiner in his letter of July 7th 2000, the probability that the blood on the piece of glass came from someone other than the suspect is smaller than 1:53.000.000. This conclusion forms the basis for the Court’s conviction that the suspect and not a third committed the robbery.”

• Report of the examiner:

“The probability for a random individual to have the same DNA-profile as the one found in the examined blood on the piece of glass ABG758, is much less than one in a million.
The current number obtained statistically from our reference database of white Dutch people is one in 53 million.”

• The Court:
  The probability that the suspect is not the donor, is smaller than 1 in 53 million (given the match).
• The examiner:
  The probability for a random donor to have the same profile is about 1 in 53 million.
  or
  If a random other person is the donor, the probability of a match is about 1 in 53 million.

The probability that

if

is about a in 53 million

The probability that

if

is very large

• Implicitly, far too low prior odds are taken
• Suppose feature occurs in 1 out of 10,000 sources
• Defense fallacy: there are another 1700 people in the Netherlands that could have left this trace. Probability that it was the suspect is therefore only 1/1700 !
• The error is that the offender population is smaller than “all Dutch” because of other evidence and information

• Which are the hypothesis words?
• Which are the observation words?
• Is the probability statement on the observation words, or on the hypothesis words?
• If the expert made a statement on the probability of the hypotheses, it is a wrong statement

In the next slides select (part) of the observation or hypothesis words, then click the corresponding button. You will get feedback and colors will indicate the right answer. Then choose if this would be a right or wrong statement for an examiner to make.

Observation Hypothesis

For a DNA-profile you can precisely calculate the probability that it came from a random person: the ‘random match probability’.

Observation Hypothesis

The probability that a random person has the same DNA-profile as the trace from the crime scene is smaller than 1 in a billion.

Waarneming Hypothese

Deze temperatuur van het overleden slachtoffer is waarschijnlijker wanneer deze overleed op het tijdstip van het scenario van de verdediging, dan op het tijdstip van de aanklager.

Waarneming Hypothese

We zagen overeenkomsten in de werktuigsporen, waardoor het iets waarschijnlijker is dat de sporen van de schroevendraaier van de verdachte kwamen dan van een andere schroevendraaier.

Waarneming Hypothese

Omdat de chromatogrammen erg op elkaar lijken, is het waarschijnlijker dat de benzine waarmee de brand is gesticht uit de jerrycan van de verdachte kwam, en niet van een andere bron.