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And / or probability worksheets

"And" and "or" are one word apart and several counters apart. These free printable worksheets give every counter a color AND a shape, which is the only kind of bag in which both questions have an answer at all.

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And / or probability
And / or probability worksheet — Two attributes, exact fractions, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

A bag of plain red and blue counters cannot ask either question: nothing is red and blue at once, and "red or blue" is every counter in it. With two attributes on each counter, "red and round" is one group of the four and "red or round" is three of them — the same bag, two words, two different numbers.

Why this sheet works

Both questions appear on the same page and often about the same bag, which is the arrangement that makes a mistake visible. On a page of only unions, a student who has read "or" as "and" still writes a fraction and gets no signal back.

How this one works

P(blue or square) from red 2 round, 2 square · blue 2 round, 6 square

2 + 2 + 2 + 6=12
2 + 2 + 2 + 6=12
2 + 2 + 6=10
10/12=5/6
  1. Count EVERYTHING first: 2 + 2 + 2 + 6 = 12 counters altogether. That is the bottom of the fraction whichever way the question is asked.
  2. "Or" means a counter counts if EITHER is true, so it is more than one group: 2 + 2 + 6 = 10. Nothing is counted twice — the groups being added do not overlap.
  3. 10 out of 12 is 5/6 in bigger pieces.

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