Advanced Addition Rule — 2 and 3 Events

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| Questions: 10 | Updated: Oct 13, 2025
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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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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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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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