Question

a pet store surveyed 420 people to see how many own a bird and how many own a cat. the venn diagram below shows the results. (each number gives the number of people who fall into that venn diagram category.) all people in the survey own a bird 96 own a cat 57 188 79 (a) how many of the people do not own a bird? people (b) how many of the people own a bird or a cat (or both)? people (c) how many of the people own a bird but do not own a cat? people

Explanation:

Part (a)

Step1: Identify non - bird groups

The people who do not own a bird are those who own a cat only and those who own neither. From the Venn diagram, the number of people who own a cat only is 188 and the number of people who own neither is 79.

Step2: Calculate the total

To find the number of people who do not own a bird, we add these two numbers: $188 + 79=267$.

Step1: Identify relevant groups

The people who own a bird or a cat (or both) are those who own a bird only, own a cat only, and own both. The number of people who own a bird only is 96, own a cat only is 188, and own both is 57.

Step2: Calculate the total

We add these three numbers: $96+57 + 188=341$.

Step1: Identify the group

The people who own a bird but do not own a cat are the ones in the "own a bird" circle but not in the overlapping region. From the Venn diagram, this number is 96.

Answer:

267

Part (b)