The Condition Names the Denominator

You'll learnto build a probability as a part over the whole the condition sets.

A probability is a part over the right whole, so the condition names the denominator: fix the world first, then count inside it. AND multiplies, OR adds, at-least-one flips to one minus none, and without replacement the pool shrinks. Points leak in taking the conditional over the wrong group, combining with the wrong operation, and reporting a look-alike instead of the probability.

8 STEPS · 6 QUICK CHECKS · the condition sets the denominator · v3

part / whole

Before you start

What you're looking at

A two-way table of 200 students split by year and choice, beside a five-move plan card.

The question

Which slice of the table is the whole, and which slice is the part?

Watch for

Watch a condition shrink the world to one row, giving the fraction a new denominator.

What the symbols mean

The grid holds every count, the edges hold the totals, and the card lists the five moves — condition, AND, OR, at-least-one, and without replacement.

The parts

1 · The setup → 2 · The denominator → 3 · The operation → 4 · Shrinking pool → 5 · The object → 6 · Transfer — then the trap and the recap

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