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The addition rule worksheets

P(A or B) = P(A) + P(B) − P(A and B). The subtraction is the whole rule, and a two-way table is where it becomes obvious: the corner cell sits in the row total AND in the column total, so adding the two counts those people twice.

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The addition rule
The addition rule worksheet — Whole percents, totals to 100, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Every question here is a survey of twenty to a hundred people, split two ways — walked or took the bus, on time or late. "What percent took the bus AND were late" is one cell. "What percent took the bus OR were late" is three, and a student who adds the row to the column without subtracting the corner gets a percent that can pass 100 — which is the arithmetic telling them what the rule is for.

Why this sheet works

The mixed setting puts both questions on the SAME table, one word apart. That is the arrangement where a wrong reading shows: on a page of unions only, a student who has read "or" as "and" still writes a number and gets no signal back.

How this one works

What percent are one or the other?

Bikes: 30·Helmet: 27
30 + 27 − 18=39
39÷60=65%
  1. "OR" means EITHER is enough, so it covers the whole Bikes row and the whole Helmet column. The row holds 30 and the column holds 27.
  2. Adding them counts the corner cell TWICE — the 18 who are both Bikes and Helmet are in the row and in the column. Subtract that overlap once.
  3. So 39 of the 60 surveyed, which is 39 ÷ 60 = 65%.

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