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Compound Counting and Probability worksheets

Reconstruct two- and three-set totals, count compound outcomes, and calculate collision probabilities by complements.

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Show favorable and total counts before forming a probability. For collisions, use the no-collision complement.

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Learning objective

What this activity builds

Translate overlapping sets and multistage selections into correct favorable and total counts before forming a probability.

Worked example

From 10 labels, three draws are made with replacement. Find the chance of a match.

1-(10/10)(9/10)(8/10)=0.28.

The complement has all three labels distinct.

Teaching notes

Make the practice count

  • Draw atomic regions before using inclusion-exclusion.
  • Keep favorable and total counts separate.
  • Use a complement for at least one collision.

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Math SheetNameScoreTeacherDateCompound Counting and ProbabilityShow favorable and total counts before forming a probability. For collisions, use the no-collision complement.1.In a group of 56, 31 chose art, 26 chose music, and 6 chose both. Find the number in exactly one group, in the union, and in neither group.Reference: Use |A union B|=|A|+|B|-|A intersection B|. Subtract the union from the total for neither.2.A survey of 42 people recorded sets A, B, and C. Totals are |A|=14, |B|=17, |C|=17, |A intersection B|=4, |A intersection C|=4, |B intersection C|=4, and |Aintersection B intersection C|=1. Find the union and neither.Reference: For three sets, add singles, subtract pair intersections, then add the triple intersection once.State the model or rule, show exact setup, then round only the final decimal.math-sheet.comPage 1 of 4
Math SheetNameScoreTeacherDateCompound Counting and ProbabilityShow favorable and total counts before forming a probability. For collisions, use the no-collision complement.3.4 selections are made independently and uniformly from 15 labels, with replacement. Find the probability that at least two selections match.Reference: Compute 1 minus the probability that all selections are distinct.4.A code uses one of 8 colors followed by one of 10 digits, with every code equally likely. A prize code uses one of 4 marked colors and one of 8 marked digits.Find the favorable count, total count, and probability.Reference: Use the multiplication rule separately for favorable outcomes and for all outcomes.State the model or rule, show exact setup, then round only the final decimal.math-sheet.comPage 2 of 4
Math SheetNameScoreTeacherDateCompound Counting and ProbabilityShow favorable and total counts before forming a probability. For collisions, use the no-collision complement.5.6 selections are made independently and uniformly from 19 labels, with replacement. Find the probability that at least two selections match.Reference: Compute 1 minus the probability that all selections are distinct.6.A survey of 41 people recorded sets A, B, and C. Totals are |A|=14, |B|=16, |C|=15, |A intersection B|=5, |A intersection C|=5, |B intersection C|=5, and |Aintersection B intersection C|=2. Find the union and neither.Reference: For three sets, add singles, subtract pair intersections, then add the triple intersection once.State the model or rule, show exact setup, then round only the final decimal.math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateCompound Counting and ProbabilityShow favorable and total counts before forming a probability. For collisions, use the no-collision complement.7.A code uses one of 6 colors followed by one of 10 digits, with every code equally likely. A prize code uses one of 2 marked colors and one of 3 marked digits.Find the favorable count, total count, and probability.Reference: Use the multiplication rule separately for favorable outcomes and for all outcomes.8.In a group of 54, 28 chose art, 28 chose music, and 6 chose both. Find the number in exactly one group, in the union, and in neither group.Reference: Use |A union B|=|A|+|B|-|A intersection B|. Subtract the union from the total for neither.State the model or rule, show exact setup, then round only the final decimal.math-sheet.comPage 4 of 4

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