Two-Set Unions, Intersections, and Probabilities Quiz

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1) For sets A and B, if |A|=28, |B|=19, and |A∩B|=7, then |A∪B| is:

Explanation

28 + 19 − 7 = 40.

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About This Quiz
Two-set Unions, Intersections, And Probabilities Quiz - Quiz

Think you can juggle counts, sets, and probabilities all at once? This quiz takes your understanding of inclusion–exclusion a step further by blending set cardinalities with real-life contexts and probability calculations. You’ll analyze situations involving students in activities, readers in libraries, and people in overlapping groups, then use union and... see moreintersection formulas to find how many are in at least one, in neither, or in both. You’ll also connect these ideas to probabilities like P(A ∪ B), P(A ∩ B), and “exactly one” events. As you work through the problems, you’ll sharpen your intuition for bounds, feasibility checks, and consistency of data — key skills for advanced counting and probability reasoning. see less

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2) If |A∪B|=50, |A|=35, and |B|=29, then |A∩B| equals:

Explanation

35 + 29 − 50 = 14.

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3) For any finite sets A and B, max(|A|,|B|) ≤ |A∪B| ≤ |A|+|B|.

Explanation

Union is at least each set, at most their sum.

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4) In a finite universe U, the number of elements in neither A nor B is:

Explanation

'Neither' means outside the union.

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5) If P(A)=0.6, P(B)=0.5, and P(A∩B)=0.3, then P(A∪B) is:

Explanation

0.6 + 0.5 − 0.3 = 0.8.

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6) In a universe of 100 elements, |A|=70 and |B|=45. Minimum |A∩B|?

Explanation

Minimum intersection = 70 + 45 − 100 = 15.

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7) Which statements are true for any finite sets A and B?

Explanation

All true except (d) when sets overlap.

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8) In a school of 90 students, 52 Drama, 41 Music, 20 both. How many in at least one?

Explanation

52 + 41 − 20 = 73.

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9) Library: 200 readers; 120 English, 90 Spanish, 50 neither. Borrow both?

Explanation

|E∪S|=150; intersection=120+90−150=60.

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10) |Aᶜ ∪ Bᶜ| = |U| − |A∩B|.

Explanation

By De Morgan, Aᶜ ∪ Bᶜ = (A∩B)ᶜ.

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11) Match expressions with meanings:

Explanation

Union=at least one; intersection=both; complements intersection=neither.

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12) Universe 60: |A|=40, |B|=35, |A∩B|=20. Neither?

Explanation

|A∪B|=55; 60−55=5.

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13) 40 people: 30 in A, 25 in B, 5 in both. Possible?

Explanation

30+25−5 = 50 > 40 impossible.

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14) Probability exactly one of A, B occurs:

Explanation

Subtract double intersection for symmetric difference.

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15) Class of 80: 55 Algebra, 50 Calculus, 15 fail both. Passed both?

Explanation

Union=65; intersection=55+50−65=40.

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For sets A and B, if |A|=28, |B|=19, and |A∩B|=7, then |A∪B|...
If |A∪B|=50, |A|=35, and |B|=29, then |A∩B| equals:
For any finite sets A and B, max(|A|,|B|) ≤ |A∪B| ≤ |A|+|B|.
In a finite universe U, the number of elements in neither A nor B is:
If P(A)=0.6, P(B)=0.5, and P(A∩B)=0.3, then P(A∪B) is:
In a universe of 100 elements, |A|=70 and |B|=45. Minimum |A∩B|?
Which statements are true for any finite sets A and B?
In a school of 90 students, 52 Drama, 41 Music, 20 both. How many in...
Library: 200 readers; 120 English, 90 Spanish, 50 neither. Borrow...
|Aᶜ ∪ Bᶜ| = |U| − |A∩B|.
Match expressions with meanings:
Universe 60: |A|=40, |B|=35, |A∩B|=20. Neither?
40 people: 30 in A, 25 in B, 5 in both. Possible?
Probability exactly one of A, B occurs:
Class of 80: 55 Algebra, 50 Calculus, 15 fail both. Passed both?
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