Inclusion–Exclusion — Advanced Practice

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| Questions: 10 | Updated: Nov 12, 2025
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1) In a survey of 80 people, 30 like cats, 50 like dogs, and 10 like neither. How many like both cats and dogs?

Explanation

|A ∪ B| = 80 − 10 = 70; 70 = 30 + 50 − x ⇒ x = 10.

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About This Quiz
Inclusionexclusion Advanced Practice - Quiz

Overlaps and intersections can complicate probability, but the inclusion–exclusion principle makes sense of it all. In this quiz, you’ll tackle advanced problems that require careful accounting of shared outcomes. Try this quiz to gain mastery over one of probability’s most powerful tools.

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2) A group of 150 students has 80 who like soccer, 70 who like basketball, and 50 who like both. How many like neither sport?

Explanation

Soccer ∪ Basketball = 80 + 70 − 50 = 100; neither = 150 − 100 = 50.

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3) P(A ∪ B) = 0.86, P(A) = 0.55, P(B) = 0.48. Find P(A ∩ B).

Explanation

0.55 + 0.48 − x = 0.86 ⇒ x = 0.17.

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4) In a group of 100 students, 60 study Math, 50 study Science, and 30 study both. How many study Math or Science?

Explanation

P(A∪B) = 60 + 50 − 30 = 80.

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5) A survey found that 40 people like tea, 35 like coffee, and 15 like both. How many people like tea only?

Explanation

Tea only = 40 − 15 = 25.

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6) In a class of 60 students, 30 are in the Art Club, 25 in the Music Club, and 10 in both. How many are in neither club?

Explanation

Art ∪ Music = 30 + 25 − 10 = 45; neither = 60 − 45 = 15.

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7) A Venn diagram shows 100 students: 45 are in A, 55 in B, and 20 in A ∩ B. How many are in A only?

Explanation

A only = 45 − 20 = 25.

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8) A Venn diagram shows 200 students: 100 take Biology, 120 take Chemistry, and 60 take both. How many take exactly one subject?

Explanation

Exactly one = (100 − 60) + (120 − 60) = 40 + 60 = 100.

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9) In a survey, 35 people like A, 40 like B, and 20 like both. How many like B only?

Explanation

B only = 40 − 20 = 20.

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10) P(A) = 0.52, P(B) = 0.47, P(A ∩ B) = 0.21. Find P(A ∪ B).

Explanation

0.52 + 0.47 − 0.21 = 0.78.

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In a survey of 80 people, 30 like cats, 50 like dogs, and 10 like...
A group of 150 students has 80 who like soccer, 70 who like...
P(A ∪ B) = 0.86, P(A) = 0.55, P(B) = 0.48. Find P(A ∩ B).
In a group of 100 students, 60 study Math, 50 study Science, and 30...
A survey found that 40 people like tea, 35 like coffee, and 15 like...
In a class of 60 students, 30 are in the Art Club, 25 in the Music...
A Venn diagram shows 100 students: 45 are in A, 55 in B, and 20 in A...
A Venn diagram shows 200 students: 100 take Biology, 120 take...
In a survey, 35 people like A, 40 like B, and 20 like both. How many...
P(A) = 0.52, P(B) = 0.47, P(A ∩ B) = 0.21. Find P(A ∪ B).
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