Exercise 3: Mapping Each Worked-Rollout Step to Its Topic — Possible Solution ==================================================================================== STEP 1: COMPUTING "ANY PROBLEM" AND "CLEAN SESSION" RATES — SAMPLE SPACES & BASIC PROBABILITY RULES (CHAPTER 2) ------------------------------ Combining two events with the union rule and then applying the complement rule to find the probability of neither happening is directly Chapter 2's own territory - no conditioning, no distributions, just the basic rules for combining and negating events. STEP 2: TESTING WHETHER TWO PROBLEM TYPES ARE RELATED — CONDITIONAL PROBABILITY & INDEPENDENCE (CHAPTER 3) ------------------------------ Comparing P(A)xP(B) against the actual joint probability to test independence, then computing P(timeout|UI error) to quantify how much one event changes the likelihood of the other, is exactly Chapter 3's own conditional-probability and independence-testing material. STEP 3: DECIDING HOW MUCH TO TRUST A MONITORING ALERT — BAYES' THEOREM (CHAPTER 4) ------------------------------ Converting a known P(alert|load issue) into the actually useful P(load issue|alert), using the law of total probability to build the denominator first, is precisely Chapter 4's own Bayes' Theorem mechanism. STEP 4: BUDGETING FOR A POSSIBLE ROLLBACK — RANDOM VARIABLES & EXPECTED VALUE (CHAPTER 5) ------------------------------ Defining a random variable over several possible costs, each with its own probability, and computing a single probability-weighted average figure to budget against, is Chapter 5's own expected-value technique. STEP 5: JUDGING HOW UNUSUAL A CANARY RESULT WOULD BE — THE BINOMIAL DISTRIBUTION (CHAPTER 6) ------------------------------ Modeling a fixed number of independent user conversions, each with the same fixed probability, and summing probabilities across several possible successful-conversion counts, is Chapter 6's own binomial distribution territory. STEP 6: JUDGING WHETHER AN INCIDENT-HEAVY WEEK IS ACTUALLY UNUSUAL — THE POISSON DISTRIBUTION (CHAPTER 7) ------------------------------ Modeling a count of rare events over a fixed time interval using only an average rate, with no fixed "number of trials" involved, is Chapter 7's own Poisson distribution material. STEP 7: READING A RESPONSE-TIME DASHBOARD CORRECTLY — THE NORMAL DISTRIBUTION & CENTRAL LIMIT THEOREM (CHAPTER 8) ------------------------------ Using z-scores and the empirical rule to compute a continuous probability range, then applying the standard-error formula to explain why an averaged dashboard metric is more stable than any single measurement, is Chapter 8's own normal-distribution and CLT territory. STEP 8: SPOTTING THE OUTLIER TRAP IN A REAL SAMPLE — DESCRIPTIVE STATISTICS (CHAPTER 9) ------------------------------ Computing the mean and median of a small set of real, already- collected response times, and recognizing how differently they react to a single outlier, is Chapter 9's own descriptive-statistics material, applied to genuine sample data rather than a known distribution. WHY THIS WORKS AS AN ANSWER ------------------------------ Each step is matched to its topic by identifying the specific mathematical operation actually being performed - combining/negating events, conditioning, inverting a conditional probability, weighting outcomes by probability, modeling fixed-trial or rate-based counts, and summarizing real data - rather than simply repeating the chapter numbers already given in the original worked rollout.