Solving for Missing Probabilities

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Reviewed by Cierra Henderson
Cierra Henderson, MBA |
K-12 Expert
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 11 | Questions: 10 | Updated: Jan 20, 2026
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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.

Submit

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.

Submit

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.

Submit

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.

Submit

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.

Submit

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.

Submit

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.

Submit

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.

Submit
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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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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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