Question

(Source: Peter Lee.) Suppose a crime has been committed. Blood is found at the scene for which there is no innocent explanation. It is of a type which is present in 1% of the population.

a. The prosecutor claims: “There is a 1% chance that the defendant would have the crime blood type if he were innocent. Thus there is a 99% chance that he guilty”. This is known as the prosecutor’s fallacy. What is wrong with this argument?

b. The defender claims: “The crime occurred in a city of 800,000 people. The blood type would be found in approximately 8000 people. The evidence has provided a probability of just 1 in 8000 that the defendant is guilty, and thus has no relevance.” This is known as the defender’s fallacy. What is wrong with this argument?

Answer 1

ANSWER::

Suppose a crime has been committed. Blood is found at the scene for which there
is no innocent explanation. It is of a type which is present in 1% of the population.
The prosecutor may then state
`There is a 1% chance that the defendant would have the crime blood type if he
were innocent. Thus there is a 99% chance that he is guilty.'
Alternatively, the defender may state
`This crime occurred in a city of 800,000 people. This blood type would be found
in approximately 8,000 people. The evidence has provided a probability of 1 in 8,000
that the defendant is guilty and thus has no relevance.'
The rst of these is known as the prosecutor's fallacy or the fallacy of the trans-
posed conditional, and as pointed out above, in essence it consists in quoting the
probability P(EjI) (E= evidence, I=innocence) instead of P(IjE). The two are
equal if and only if the prior probability P(I) of innocence is taken as 1
b, which is
scarcely in accord with a presumption of innocence. The second of these is known as
the defender's fallacy which consists of reporting P(GjE) (G=guilt), without regard
to P(G).

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