Practice Addition Rule in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The addition rule finds the probability that at least one of two events occurs. It adds the probabilities of the two events and then subtracts any overlap so the shared outcomes are not counted twice.

If you want “A or B,” start by adding A and B. Then fix the double-counting by removing the part that belongs to both events.

Showing a random 20 of 50 problems.

Example 1

medium
Using the same survey (70%70\% phone, 40%40\% laptop, 30%30\% both), find the percent who own neither.

Example 2

medium
P(B)=0.55P(B)=0.55, P(A∩B)=0.20P(A\cap B)=0.20, P(AâˆȘB)=0.85P(A\cup B)=0.85. Find P(A)P(A).

Example 3

challenge
Three events A,B,CA,B,C are pairwise disjoint with probabilities 0.2,0.3,0.40.2,0.3,0.4. Find P(AâˆȘBâˆȘC)P(A\cup B\cup C) and the probability of none.

Example 4

easy
P(A)=0.6P(A)=0.6, P(B)=0.5P(B)=0.5, P(AâˆȘB)=0.8P(A\cup B)=0.8. Find P(A∩B)P(A\cap B).

Example 5

challenge
A coin is flipped 3 times. Find P(at least one head)P(\text{at least one head}) two ways and confirm they agree.

Example 6

medium
In a class, 60%60\% like pizza, 50%50\% like tacos, and 30%30\% like both. Find the percent who like at least one.

Example 7

easy
A card is drawn. Find P(king or queen)P(\text{king or queen}).

Example 8

medium
A spinner has four disjoint regions with probabilities 0.20,0.30,0.10,0.400.20, 0.30, 0.10, 0.40. Find P(first or third region)P(\text{first or third region}).

Example 9

medium
From integers 1 to 50, find P(prime or even)P(\text{prime or even}). (Note: 2 is even and prime.)

Example 10

challenge
P(A)=0.5P(A)=0.5, P(B)=0.6P(B)=0.6. Find the smallest possible P(AâˆȘB)P(A\cup B).

Example 11

hard
Suppose P(A)=0.45P(A)=0.45, P(B)=0.55P(B)=0.55, and A,BA,B are independent. Find P(exactly one of A,B)P(\text{exactly one of }A,B).

Example 12

easy
From a deck, find P(heart or spade)P(\text{heart or spade}).

Example 13

medium
A weather model says P(rain)=0.4P(\text{rain})=0.4, P(wind)=0.5P(\text{wind})=0.5, P(rain and wind)=0.3P(\text{rain and wind})=0.3. Find P(rain or wind)P(\text{rain or wind}).

Example 14

easy
P(A)=0.45P(A)=0.45, P(B)=0.35P(B)=0.35, disjoint. Find P(AâˆȘB)P(A\cup B).

Example 15

medium
From a deck, find P(red or king)P(\text{red or king}).

Example 16

medium
P(A)=0.7P(A)=0.7, P(A∩B)=0.2P(A\cap B)=0.2, P(AâˆȘB)=0.9P(A\cup B)=0.9. Find P(B)P(B).

Example 17

challenge
Events A,B,CA,B,C satisfy P(A)=P(B)=P(C)=0.5P(A)=P(B)=P(C)=0.5, pairwise independent, and P(A∩B∩C)=0.1P(A\cap B\cap C)=0.1. Find P(AâˆȘBâˆȘC)P(A\cup B\cup C).

Example 18

easy
A die is rolled. Find P(even or 6)P(\text{even or }6).

Example 19

medium
Of 100 students, 40 take French, 30 take Spanish, 10 take both. How many take at least one language?

Example 20

easy
Events AA and BB are mutually exclusive with P(A)=0.2P(A)=0.2, P(B)=0.5P(B)=0.5. Find P(AâˆȘB)P(A\cup B).
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