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Independent events worksheets

Two events are independent when knowing one tells you nothing about the other, and that has a test you can run: the share who are BOTH should be the share who are A times the share who are B. These free printable worksheets give the table and ask for the verdict.

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Independent events
Independent events worksheet — Totals of 100, whole percents, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Every survey on these sheets is of exactly 100 people, and that is deliberate rather than lazy: at a total of a hundred the counts in the table already ARE percents, so the comparison is between two numbers a student can read and multiply without a division in the way. The arithmetic is not what this standard is about — noticing that the overlap can be PREDICTED from the two margins is.

Why this sheet works

Half of every page is independent and half is not. A sheet where the answer is the same every time is one a student can pass without looking, so both verdicts are always dealt.

How this one works

Are the two events independent?

P = 40%·P = 70%
40% × 70%=28%
table 28%=predicted 28%→Independent
  1. 40 of the 100 are Team A and 70 are Won, so P(Team A) is 40% and P(Won) is 70%.
  2. If the two had nothing to do with each other, the share who are BOTH would be one share OF the other: 40% × 70% = 28%.
  3. The table shows 28 of the 100 in that corner — exactly the 28% predicted. Knowing one tells you nothing about the other, so they ARE independent.

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