Exercise 1: Probability Question or Statistics Question? — Possible Solution ==================================================================== (A) A FAIR DIE, CHANCE OF ROLLING A 6 — PROBABILITY ------------------------------ The model is already fully known and given (a fair six-sided die, each face equally likely) before any question is asked. This is reasoning FORWARD from a known model to a predicted outcome - exactly this chapter's own definition of a probability question. No data was collected; nothing needs to be inferred. (B) 1,000 RECORDED SERVER RESPONSE TIMES, THEIR AVERAGE — STATISTICS ------------------------------ This starts from actual observed data (1,000 real recorded values) and asks for a summary computed directly from that data. There's no prior "model" being used to predict anything - the average is simply calculated from what was actually recorded. This is squarely a statistics question per this chapter's own definition. (C) KNOWN 2% DEFECT RATE, EXPECTED DEFECTS IN A BATCH OF 500 — PROBABILITY ------------------------------ The defect rate (2%) is stated as already known, not something being estimated from a batch of data. Given that known rate, the question asks what outcome to expect: 500 x 0.02 = 10 expected defective units. This is reasoning forward from a known model (the 2% rate) to a predicted outcome - a probability question. (D) LAST MONTH'S ACTUAL INCIDENT COUNTS, ESTIMATE THE TRUE UNDERLYING RATE — STATISTICS ------------------------------ Here the actual counts are the starting point (real, already-occurred data), and the "true underlying rate" is unknown and needs to be inferred FROM that data. This is reasoning backward from observed data to an inferred model - a statistics question, per this chapter's own definition, even though it superficially resembles part (C). WHY THIS WORKS AS AN ANSWER ------------------------------ Each classification is made by checking which direction the reasoning actually runs - starting from an already-known model and predicting an outcome (probability), or starting from real observed data and inferring an unknown model (statistics) - per this chapter's own distinction, rather than classifying based on surface-level similarity between (C) and (D), which look alike but reason in opposite directions.