Exercise 1: A Second Round of Fraud-Detection Evidence — Possible Solution
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GIVEN
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Round 1 posterior (from Probability & Statistics Fundamentals Ch.4):
  P(fraud | flagged) ~= 0.0454

This becomes the round-2 prior. New evidence:
  P(location | fraud) = 0.70
  P(location | not fraud) = 0.10

STEP 1: THE TOTAL PROBABILITY OF THE NEW EVIDENCE
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Using this chapter's own sequential-updating method, with prior =
0.0454:

P(location) = P(location|fraud) x prior + P(location|not fraud) x (1-prior)
            = (0.70)(0.0454) + (0.10)(0.9546)
            = 0.03178 + 0.09546
            = 0.12724

STEP 2: APPLYING BAYES' THEOREM AGAIN
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P(fraud | flagged AND location) = [P(location|fraud) x prior] / P(location)
                                  = 0.03178 / 0.12724
                                  ~= 0.2497 (about 25%)

STEP 3: THE FULL UPDATE SEQUENCE
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Prior (0.1%) -> after "flagged" (~4.5%) -> after "unusual location" (~25%)

Two corroborating signals together raised the belief this transaction
is fraudulent from a 0.1% baseline all the way to roughly 1 in 4 - a
dramatic update, even though the transaction is still more likely NOT
fraudulent than fraudulent at this point.

WHY THIS WORKS AS AN ANSWER
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The round-1 posterior is correctly used as the round-2 prior per this
chapter's own sequential-updating method, the law of total probability
and Bayes' Theorem are applied a second time exactly as shown in the
chapter's own spam-filter example, and the full three-step belief
progression is stated explicitly to show the cumulative effect of both
pieces of evidence together.