Nothing in this chapter carries a unit, so the usual unit check has nothing to grab. Its replacement is the range check, and it is just as absolute. A probability $P$ is a share of certainty: it lives in $0 \le P \le 1$, 0 for never and 1 for always, and a value outside that corridor is wrong the way a negative mass is wrong — no appeal, no rounding excuse.

Two impostors sit beside it. Odds $O$ compare the event to its own failure rather than to everything: $O = \dfrac{P}{1 - P}$, read aloud O equals P over one minus P. Odds have no ceiling — a 0.75 chance is odds of 3, quoted “3 to 1”. And a count is neither: a plain whole number of outcomes, the raw material a probability is later built from. In $P = \dfrac{f}{n}$, the letter $f$ is the count of favourable outcomes and $n$ the count of all equally likely outcomes; both are tallies, and only their ratio is a chance.

This lesson computes nothing. It asks one thing over and over: which of the three is this number? Get that reflex right and half the chapter's wrong answers never get written down.