Exercise 2: Two Genuinely Different Probability Questions — Possible Solution
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"The probability of this evidence, assuming innocence" asks: if Sally
Clark were genuinely innocent and both deaths were natural, how likely
would it be to observe exactly this evidence (two SIDS deaths in one
family)? Meadow's real 1-in-73-million figure was an attempt to answer
this question - however flawed the calculation itself was.

"The probability of innocence, given this evidence" asks a completely
different question: given that we've actually observed two deaths in
this specific family, how likely is it that Clark is innocent? This is
the real question a jury actually needs answered to decide guilt, and
it requires factoring in something the first question never
considers: how common wrongful accusation is in general, compared to
how common a genuine, tragic coincidence of two natural deaths in one
family actually is, using real prior information beyond just the
death statistics.

The prosecutor's fallacy is treating the first, much narrower number
(a tiny probability of the evidence occurring under innocence) as
though it directly answers the second, genuinely different question
(the probability of innocence given the evidence). A very small chance
that something would happen if a person were innocent does not, on its
own, tell you the probability that the person actually is innocent -
that depends on comparing it honestly against the also-real
possibility of a false accusation, not just asserting the first number
as the answer to the second question.

ANSWER: "Probability of the evidence, assuming innocence" asks how
likely two SIDS deaths would be if Clark were innocent - the question
Meadow's 1-in-73-million figure attempted to answer. "Probability of
innocence, given the evidence" asks something genuinely different: how
likely is Clark actually innocent, given what was observed - which
requires weighing that number against the real likelihood of a false
accusation, not simply treating the first number as though it directly
answered the second.

WHY THIS WORKS AS AN ANSWER
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This clearly distinguishes the two probability questions using the
chapter's own real case, explaining precisely what the prosecutor's
fallacy conflates rather than only naming that a conflation occurred.