Advanced Addition Rule — 2 and 3 Events

  • 11th Grade
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Cierra Henderson, MBA |
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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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| Questions: 10 | Updated: Jan 20, 2026
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1) Given P(A)=0.6, P(B)=0.5, and P(A∩B)=0.4, find P(A∪B).

Explanation

P(A∪B)=0.6+0.5−0.4=0.7

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About This Quiz
Advanced Addition Rule 2 and 3 Events - Quiz

Probability gets trickier with multiple events. In this quiz, you’ll apply the addition rule for two and three events, making sure to account for overlaps correctly. Take this quiz to master advanced scenarios in probability.

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2) P(A)=0.45, P(B)=0.4, and P(A∩B)=0.25. Find P(A∪B).

Explanation

0.45+0.4−0.25=0.6

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3) If |A|=40, |B|=30, |A∩B|=10, and total n=100, find P(A∪B).

Explanation

(40+30−10)/100=60/100=0.6

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4) If P(A)=0.55, P(B)=0.35, and P(A∩B)=0.25, find P(A∪B).

Explanation

0.55+0.35−0.25=0.65

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5) Given P(A)=0.5, P(B)=0.3, P(C)=0.2, P(A∩B)=0.1, P(A∩C)=0.05, P(B∩C)=0.05, and P(A∩B∩C)=0.02, find P(A∪B∪C).

Explanation

0.5+0.3+0.2−0.1−0.05−0.05+0.02=0.63

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6) If |A|=50, |B|=60, |C|=30, |A∩B|=20, |A∩C|=15, |B∩C|=10, |A∩B∩C|=5, total n=200. Find P(A∪B∪C).

Explanation

(50+60+30−20−15−10+5)/200=120/200=0.6

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7) P(A)=0.4, P(B)=0.35, P(A∩B)=0.15, P(C)=0.25, P(A∩C)=0.1, P(B∩C)=0.05, P(A∩B∩C)=0.02. Find P(A∪B∪C).

Explanation

0.4+0.35+0.25−0.15−0.1−0.05+0.02=0.68

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8) If |A|=70, |B|=60, |A∩B|=50, total n=100. Find P(A∪B).

Explanation

(70+60−50)/100=80/100=0.8

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9) P(A)=0.7, P(B)=0.5, P(A∩B)=0.45. Find P(A∪B).

Explanation

0.7+0.5−0.45=0.75

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10) If |A|=90, |B|=85, |C|=60, |A∩B|=50, |A∩C|=40, |B∩C|=30, |A∩B∩C|=20, total n=200. Find P(A∪B∪C).

Explanation

(90+85+60−50−40−30+20)/200=195/200=0.975

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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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Given P(A)=0.6, P(B)=0.5, and P(A∩B)=0.4, find P(A∪B).
P(A)=0.45, P(B)=0.4, and P(A∩B)=0.25. Find P(A∪B).
If |A|=40, |B|=30, |A∩B|=10, and total n=100, find P(A∪B).
If P(A)=0.55, P(B)=0.35, and P(A∩B)=0.25, find P(A∪B).
Given P(A)=0.5, P(B)=0.3, P(C)=0.2, P(A∩B)=0.1, P(A∩C)=0.05,...
If |A|=50, |B|=60, |C|=30, |A∩B|=20, |A∩C|=15, |B∩C|=10,...
P(A)=0.4, P(B)=0.35, P(A∩B)=0.15, P(C)=0.25, P(A∩C)=0.1,...
If |A|=70, |B|=60, |A∩B|=50, total n=100. Find P(A∪B).
P(A)=0.7, P(B)=0.5, P(A∩B)=0.45. Find P(A∪B).
If |A|=90, |B|=85, |C|=60, |A∩B|=50, |A∩C|=40, |B∩C|=30,...
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