Exercise 2: Probability & Statistics Beyond Machine Learning — Possible Solution
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THE CLAIM BEING CHALLENGED
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The colleague's claim is that probability and statistics only matter
for data science or machine learning work. This chapter's own five-
connections table shows at least two clear counterexamples where this
reasoning is doing real work with no ML involved at all.

COUNTEREXAMPLE 1: RETRY LOGIC AND ERROR BUDGETS
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A system that retries a failing operation up to three times, where
each attempt independently succeeds 90% of the time, relies directly
on probability rules to reason about the combined chance of total
failure - no model training, no dataset, no ML tooling anywhere in
sight. This is ordinary distributed-systems engineering, and it's
built entirely on the same probability rules this chapter covers.

COUNTEREXAMPLE 2: MONITORING DASHBOARDS
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Every "average response time" or "average error rate" panel on an
ordinary monitoring dashboard is a direct application of descriptive
statistics - summarizing real recorded data into a single
representative number. This is standard operational tooling used by
any team running a service, entirely independent of whether that team
does any machine learning work at all.

WHY THIS WORKS AS AN ANSWER
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It directly challenges the colleague's premise using two of this
chapter's own five connections - probability rules in retry logic and
descriptive statistics in monitoring dashboards - both of which are
genuinely standalone, everyday engineering use cases with no
dependency on machine learning, rather than simply restating that ML
also uses probability and statistics (which the colleague already
believes).