Exercise 3: Mapping Real System-Design Scenarios to Topics — Possible Solution
====================================================================

(A) A RETRY MECHANISM, EACH ATTEMPT 90% SUCCESSFUL — PROBABILITY
RULES & CONDITIONAL PROBABILITY (CHAPTERS 2-3)
------------------------------
Each attempt fails independently with probability 0.1 (10%). The
chance all three independent attempts fail is found by multiplying
the individual failure probabilities together:

  0.1 x 0.1 x 0.1 = 0.001 = 0.1%

Combining probabilities of independent events by multiplying them is
exactly this chapter's own probability-rules and independence
territory (Chapters 2-3), not a topic that needs Bayes' Theorem or a
named distribution to answer.

(B) FRAUD DETECTION COMBINING SEVERAL WEAK SIGNALS INTO ONE RISK
SCORE — BAYES' THEOREM (CHAPTER 4)
------------------------------
Taking several individually unreliable pieces of evidence (an unusual
login location, an unusual purchase amount, a new device) and
combining them into one updated overall probability of fraud is
precisely the kind of "update a probability given new evidence"
reasoning this chapter's own connections table names Bayes' Theorem
for directly - the same mechanism spam filters use.

(C) A DASHBOARD SHOWING "AVERAGE RESPONSE TIME" OVER THE LAST HOUR —
DESCRIPTIVE STATISTICS (CHAPTER 9)
------------------------------
This is a direct summary computed from real recorded data (actual
response times over the last hour), condensed into a single
representative number. That's exactly this chapter's own descriptive-
statistics connection - and, per this chapter's own note, the exact
kind of average that can quietly hide a real spike, a caution already
covered from the diagnostic side in the Technical Support subject's
own material.

WHY THIS WORKS AS AN ANSWER
------------------------------
Each scenario is matched to its topic by identifying the specific
reasoning actually being performed - multiplying independent
probabilities, updating a probability using multiple pieces of
evidence, or summarizing real recorded data - rather than by surface-
level keyword matching alone.