This is the boss. No calculator — every draw is pinned so the arithmetic fits in your head, and the powers are small on purpose ($0.9^{2} = 0.81$, $0.9^{3} = 0.729$, $0.8^{2} = 0.64$). One table, one long problem, and every answer feeds the next: how many plays exist, then the chance one play wins, then the chance the evening produces at least one win, then what a single ticket is actually worth. Write each line down — one early slip rides all the way to the verdict.

The chapter's whole argument lives in this cascade. Counting sets the denominator; the classical rule turns that count into a chance; the complement turns one play into a whole evening; and expected value turns a chance into money. The last line is not a number — it is a DECISION, and the arithmetic above it is the only honest way to reach one. 5★ under par here is the chapter crown. Clock in.