Question

question 2 of 6 (1 point) | question attempt: 1 of unlimited a pet store conducted a survey to gather information about the types of pets people... 664 people were surveyed in all; 388 of the people own a cat; 331 of the people own a bird; 210 of the people own both a cat and a bird; 103 of the people own both a cat and a fish; 119 of the people own both a bird and a fish; 67 of the people own all three types of pets (cat, bird, fish); 43 of the people dont own any of these three types of pets (cat, bird, fish). construct a venn diagram illustrating these results. then answer the question. image of venn diagram with all people in the survey, own a cat, own a bird, own a fish circles and boxes how many of the pe... but dont own a fish 143 people

Explanation:

To solve the problem of finding the number of people who own a cat or a bird but do not own a fish, we use the principle of inclusion - exclusion for sets.

Step 1: Find the number of people who own only a cat and a bird

We know that the number of people who own both a cat and a bird is \(n(C\cap B) = 210\), and the number of people who own all three pets (cat, bird, fish) is \(n(C\cap B\cap F)=67\). The number of people who own only a cat and a bird is given by:
\(n(\text{only } C\cap B)=n(C\cap B)-n(C\cap B\cap F)\)
\(n(\text{only } C\cap B)=210 - 67=143\)

Step 2: Find the number of people who own only a cat

We know that the number of people who own a cat is \(n(C) = 388\), the number of people who own a cat and a fish is \(n(C\cap F) = 103\), and the number of people who own all three pets is \(n(C\cap B\cap F) = 67\), and the number of people who own only a cat and a bird is \(n(\text{only } C\cap B)=143\)

The number of people who own only a cat is:
\(n(\text{only } C)=n(C)-n(C\cap F)-n(\text{only } C\cap B)-n(C\cap B\cap F)\)
\(n(\text{only } C)=388- 103-143 - 67\)
\(n(\text{only } C)=388-(103 + 143+67)\)
\(n(\text{only } C)=388 - 313=75\)

Step 3: Find the number of people who own only a bird

We know that the number of people who own a bird is \(n(B)=331\), the number of people who own a bird and a fish is \(n(B\cap F) = 119\), the number of people who own all three pets is \(n(C\cap B\cap F)=67\) and the number of people who own only a cat and a bird is \(n(\text{only } C\cap B) = 143\)

The number of people who own only a bird is:
\(n(\text{only } B)=n(B)-n(B\cap F)-n(\text{only } C\cap B)-n(C\cap B\cap F)\)
\(n(\text{only } B)=331-119 - 143-67\)
\(n(\text{only } B)=331-(119 + 143+67)\)
\(n(\text{only } B)=331 - 329 = 2\)

Step 4: Find the number of people who own a cat or a bird but not a fish

The number of people who own a cat or a bird but not a fish is the sum of the number of people who own only a cat, only a bird, and only a cat and a bird.

\(N=n(\text{only } C)+n(\text{only } B)+n(\text{only } C\cap B)\)
\(N = 75+2 + 143\)
\(N=220\)

Answer:

The number of people who own a cat or a bird but do not own a fish is \(\boldsymbol{220}\)