Solving for Missing Probabilities

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| By Thames
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Quizzes Created: 7288 | Total Attempts: 9,526,515
| Questions: 10 | Updated: Nov 12, 2025
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1) P(A) = 0.45, P(B) = 0.35, P(A ∪ B) = 0.70. Find P(A ∩ B).

Explanation

P(A ∩ B) = P(A) + P(B) − P(A ∪ B) = 0.45 + 0.35 − 0.70 = 0.10.

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About This Quiz
Solving For Missing Probabilities - Quiz

Sometimes in probability, not all the numbers are given—but the missing values can be found! In this quiz, you’ll work on solving for unknown probabilities using given information and logical reasoning. Take this quiz to strengthen your detective skills in probability.

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2) P(A) = 0.60, P(B) = 0.50, P(A ∪ B) = 0.85. Find P(A ∩ B).

Explanation

0.60 + 0.50 − 0.85 = 0.25.

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3) P(A) = 0.60, P(B) = 0.50, P(A ∩ B) = 0.25. Find P(A ∪ B).

Explanation

P(A ∪ B) = 0.60 + 0.50 − 0.25 = 0.85.

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4) P(A ∪ B) = 0.92, P(A) = 0.65, P(B) = 0.50. Find P(A ∩ B).

Explanation

0.65 + 0.50 − 0.92 = 0.23.

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5) P(A) = 0.80, P(B) = 0.70, P(A ∩ B) = 0.60. Find P(A ∪ B).

Explanation

0.80 + 0.70 − 0.60 = 0.90.

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6) P(A) = 0.30, P(B) = 0.25, P(A ∩ B) = 0.15. Find P(A ∪ B).

Explanation

0.30 + 0.25 − 0.15 = 0.40.

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7) P(A ∪ B) = 0.78, P(A) = 0.48, P(A ∩ B) = 0.20. Find P(B).

Explanation

P(B) = 0.78 − 0.48 + 0.20 = 0.50.

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8) P(A ∪ B) = 0.62, P(B) = 0.41, P(A ∩ B) = 0.12. Find P(A).

Explanation

P(A) = 0.62 − 0.41 + 0.12 = 0.33.

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9) P(A) = 0.58, P(B) = 0.46, P(A ∩ B) = 0.29. Find P(A ∪ B).

Explanation

0.58 + 0.46 − 0.29 = 0.75.

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10) P(A) = 0.45, P(B) = 0.40, P(A ∪ B) = 0.72. Find P(A ∩ B).

Explanation

0.45 + 0.40 − 0.72 = 0.13.

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P(A) = 0.45, P(B) = 0.35, P(A ∪ B) = 0.70. Find P(A ∩ B).
P(A) = 0.60, P(B) = 0.50, P(A ∪ B) = 0.85. Find P(A ∩ B).
P(A) = 0.60, P(B) = 0.50, P(A ∩ B) = 0.25. Find P(A ∪ B).
P(A ∪ B) = 0.92, P(A) = 0.65, P(B) = 0.50. Find P(A ∩ B).
P(A) = 0.80, P(B) = 0.70, P(A ∩ B) = 0.60. Find P(A ∪ B).
P(A) = 0.30, P(B) = 0.25, P(A ∩ B) = 0.15. Find P(A ∪ B).
P(A ∪ B) = 0.78, P(A) = 0.48, P(A ∩ B) = 0.20. Find P(B).
P(A ∪ B) = 0.62, P(B) = 0.41, P(A ∩ B) = 0.12. Find P(A).
P(A) = 0.58, P(B) = 0.46, P(A ∩ B) = 0.29. Find P(A ∪ B).
P(A) = 0.45, P(B) = 0.40, P(A ∪ B) = 0.72. Find P(A ∩ B).
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